id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
700,054 | KOU-1.63 | Kourovka Notebook Problem 1.63 | A group $G$ is called *dense* if it has no proper
isolated subgroups other than its trivial subgroup.
a) Do there exist dense torsion-free groups that are not
locally cyclic?
b) Suppose that any two non-trivial elements $x$ and $y$ of a
torsion-free group $G$ satisfy the relation $ x^k = y^l$, where
$k$ and $l$ are n... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.63.
Proposed by: P. G. Kontorovich
Published resolution:
a) Yes, such groups do exist; b) Not necessarily (S. I. Adian, *Math.
USSR--Izv.*, **5** (1971), 475--484). | 2 | solved | P. G. Kontorovich | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: a) Yes, such groups do exist; b) Not necessarily (S. I. Adian, *Math.\nUSSR--Izv.*, **5** (1971), 475--484)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,055 | KOU-1.64 | Kourovka Notebook Problem 1.64 | A torsion-free group is said to be *separable* if it can
be represented as the set-theoretic union of two of its proper
subsemigroups. Is every $R$-group separable? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.64.
Proposed by: P. G. Kontorovich
Published resolution:
No (S. J. Pride, J. Wiegold, *Bull. London Math. Soc.*, **9**
(1977),
36--37). | 2 | solved | P. G. Kontorovich | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No (S. J. Pride, J. Wiegold, *Bull. London Math. Soc.*, **9**\n(1977),\n36--37)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,056 | KOU-1.65 | Kourovka Notebook Problem 1.65 | Is the class of groups of abelian extensions of
abelian groups closed under taking direct sums $(A,B) \mapsto A
\oplus B$? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 1st issue (1965), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 1.65.
Proposed by: L. Ya. Kulikov | 2 | open | L. Ya. Kulikov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,057 | KOU-1.66 | Kourovka Notebook Problem 1.66 | Suppose that $T$ is a periodic abelian group, and
${\mathfrak{m}}$ an uncountable cardinal number. Does there always
exist an abelian torsion-free group $U(T,{\mathfrak{m}})$ of
cardinality ${\mathfrak{m}}$ with the following property: for any
abelian torsion-free group $A$ of cardinality $\leq {\mathfrak{m}}$,
the equ... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.66.
Proposed by: L. Ya. Kulikov
Published resolution:
No, not always. There is a model of ZFC in which for a certain
class of cardinals ${\mathfrak{m}}$ the answer is negative (S... | 2 | solved | L. Ya. Kulikov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No, not always. There is a model of ZFC in which for a certain\nclass of cardinals ${\\mathfrak{m}}$ the answer is negative (S. Shelah,\nL. Str\\\"ungmann, *J. L... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,058 | KOU-1.67 | Kourovka Notebook Problem 1.67 | Suppose that $G$ is a finitely presented group,
$F$ a free group whose rank is equal to the minimal number of
generators of $G$, with a fixed homomorphism of $F$ onto $G$ with
kernel $N$. Find a complete system of invariants of the
factor-group of $N$ by the commutator subgroup $[F,N]$. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 1st issue (1965), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 1.67.
Proposed by: L. Ya. Kulikov | 2 | open | L. Ya. Kulikov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,059 | KOU-1.68 | Kourovka Notebook Problem 1.68 | (A. Tarski). Let ${\mathfrak{K}}$ be a class of groups and $Q{\mathfrak{K}}$ the class of all homomorphic images of groups from ${\mathfrak{K}}$. If ${\mathfrak{K}}$ is axiomatizable, does it follow that $Q{\mathfrak{K}}$ is? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.68.
Proposed by: Yu. I. Merzlyakov
Published resolution:
Not always (F. Clare, *Algebra Universalis*, **5**
(1975), 120--124). | 2 | solved | Yu. I. Merzlyakov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always (F. Clare, *Algebra Universalis*, **5**\n(1975), 120--124)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,060 | KOU-1.69 | Kourovka Notebook Problem 1.69 | (B. I. Plotkin). Do there exist locally nilpotent torsion-free
groups without the property $RN^*$? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.69.
Proposed by: Yu. I. Merzlyakov
Published resolution:
Yes, such groups do exist (E. M. Levich, A. I. Tokarenko, *Siberian
Math. J.*, **11** (1970), 1033--1034; \ A. I. Tokaren... | 2 | solved | Yu. I. Merzlyakov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, such groups do exist (E. M. Levich, A. I. Tokarenko, *Siberian\nMath. J.*, **11** (1970), 1033--1034; \\ A. I. Tokarenko, *Trudy Rizhsk. Algebr. Sem.*, Riga... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,061 | KOU-1.70 | Kourovka Notebook Problem 1.70 | Let $p$ be a prime number and let $G$ be the group of all matrices of the
form {\small $\left( \begin{array}{cc} 1+p\alpha & p\beta\\
p\gamma & 1+p\delta \end{array}\right)$}, where $\alpha$, $\beta$,
$\gamma$, $\delta$ are rational numbers with denominators coprime
to $p$. Does $G$ have the property $ \overline{\! RN}... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.70.
Proposed by: Yu. I. Merzlyakov
Published resolution:
Yes, it does (G. A. Noskov, *Siberian Math. J.*, **14**
(1973), 475--477). | 2 | solved | Yu. I. Merzlyakov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it does (G. A. Noskov, *Siberian Math. J.*, **14**\n(1973), 475--477)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,062 | KOU-1.71 | Kourovka Notebook Problem 1.71 | Let $G$ be a connected algebraic group over an algebraically
closed field. Is the number of conjugacy classes of maximal
soluble subgroups of $G$ finite? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.71.
Proposed by: V. P. Platonov
Published resolution:
Yes, it is (V. P. Platonov, *Siberian Math. J.*, **10**
(1969), 800--804). | 2 | solved | V. P. Platonov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it is (V. P. Platonov, *Siberian Math. J.*, **10**\n(1969), 800--804)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,063 | KOU-1.72 | Kourovka Notebook Problem 1.72 | D. Hertzig has shown that a connected algebraic group over an
algebraically closed field is soluble if it has a rational regular
automorphism. Is this result true for an arbitrary field? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.72.
Proposed by: V. P. Platonov
Published resolution:
No (V. P. Platonov, *Soviet Math. Dokl.*, **7** (1966),
825--829). | 2 | solved | V. P. Platonov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No (V. P. Platonov, *Soviet Math. Dokl.*, **7** (1966),\n825--829)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,064 | KOU-1.73 | Kourovka Notebook Problem 1.73 | Are there only finitely many conjugacy classes of maximal
periodic subgroups in a finitely generated linear group over the
integers? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.73.
Proposed by: V. P. Platonov
Published resolution:
Not always. The extension $H$ of the free group on free generators
$a,b$ by the automorphism $ \varphi :a\rightarrow
a^{-1},... | 2 | solved | V. P. Platonov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always. The extension $H$ of the free group on free generators\n$a,b$ by the automorphism $ \\varphi :a\\rightarrow\na^{-1},\\;\\;b\\rightarrow b$ is a linea... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,065 | KOU-1.74 | Kourovka Notebook Problem 1.74 | Describe all minimal topological groups, that is,
non-discrete groups all of whose closed subgroups are discrete. The
minimal locally compact groups can be described without much effort.
At the same time, the problem is probably complicated in the general
case. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 1st issue (1965), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 1.74.
Proposed by: V. P. Platonov | 2 | open | V. P. Platonov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,066 | KOU-1.75 | Kourovka Notebook Problem 1.75 | Classify the infinite simple periodic
linear groups over a
field of characteristic $p > 0$. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.75.
Proposed by: V. P. Platonov
Published resolution:
They are classified for every $p$ mod CFSG (V. V. Belyaev, in: *Investigations in Group Theory*, Sverdlovsk, UNC AN SSSR, 19... | 2 | solved | V. P. Platonov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: They are classified for every $p$ mod CFSG (V. V. Belyaev, in: *Investigations in Group Theory*, Sverdlovsk, UNC AN SSSR, 1984,\n39--50 (Russian); \\ A. V. Borov... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,067 | KOU-1.76 | Kourovka Notebook Problem 1.76 | Does there exist a simple, locally nilpotent, locally compact,
topological group? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.76.
Proposed by: V. P. Platonov
Published resolution:
No (I. V. Protasov, *Soviet Math. Dokl.*, **19** (1978),
487--489). | 2 | solved | V. P. Platonov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No (I. V. Protasov, *Soviet Math. Dokl.*, **19** (1978),\n487--489)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,068 | KOU-1.78 | Kourovka Notebook Problem 1.78 | Let a group $G$ be the product of two
divisible abelian $p $-groups of finite rank. Is then $G$ itself a
divisible abelian $p $-group of finite rank? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.78.
Proposed by: N. F. Sesekin
Published resolution:
Yet, it is (N. F. Sesekin, *Siberian Math. J.*, **9**
(1968), 1070--1072). | 2 | solved | N. F. Sesekin | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yet, it is (N. F. Sesekin, *Siberian Math. J.*, **9**\n(1968), 1070--1072)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,069 | KOU-1.80 | Kourovka Notebook Problem 1.80 | Does there exist a finite simple group whose Sylow 2-subgroup
is a direct product of quaternion groups? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.80.
Proposed by: A. I. Starostin
Published resolution:
No (G. Glauberman, *J. Algebra*, **4** (1966), 403--420). | 2 | solved | A. I. Starostin | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No (G. Glauberman, *J. Algebra*, **4** (1966), 403--420)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,070 | KOU-1.81 | Kourovka Notebook Problem 1.81 | The *width* of a group $G$ is, by definition, the
smallest cardinal $ m = m(G)$ with the property that any
subgroup of $G$ generated by a finite set $S\subseteq G$ is
generated by a subset of $S$ of cardinality at most $m$.
a) Does a group of finite width satisfy the minimum condition
for subgroups?
b) Does a group w... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.81.
Proposed by: L. N. Shevrin
Published resolution:
a) Not always (S. V. Ivanov, *Geometric methods in the study
of groups with given subgroup properties*, Cand. Diss.,
Moscow U... | 2 | solved | L. N. Shevrin | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: a) Not always (S. V. Ivanov, *Geometric methods in the study\nof groups with given subgroup properties*, Cand. Diss.,\nMoscow Univ., Moscow, 1988 (Russian)).\n\n... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,071 | KOU-1.82 | Kourovka Notebook Problem 1.82 | Two sets of identities are said to be *equivalent* if they
determine the same variety of groups. Construct an infinite set
of identities which is not equivalent to any finite one. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.82.
Proposed by: A. L. Shmel'kin
Published resolution:
This was done (S. I. Adian, *Math. USSR--Izv.*, **4**
(1970), 721--739). | 2 | solved | A. L. Shmel'kin | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: This was done (S. I. Adian, *Math. USSR--Izv.*, **4**\n(1970), 721--739)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,072 | KOU-1.83 | Kourovka Notebook Problem 1.83 | Does there exist a simple group, the orders of whose elements
are unbounded, in which a non-trivial identity relation
holds? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.83.
Proposed by: A. L. Shmel'kin
Published resolution:
Yes, such groups do exist (V. S. Atabekyan, Dep. no. 5381-V86, VINITI,
Moscow, 1986 (Russian)). | 2 | solved | A. L. Shmel'kin | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, such groups do exist (V. S. Atabekyan, Dep. no. 5381-V86, VINITI,\nMoscow, 1986 (Russian))."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,073 | KOU-1.84 | Kourovka Notebook Problem 1.84 | Is it true that
a polycyclic group $G$ is
residually a finite $p $-group if and only if $G$ has a
nilpotent normal torsion-free subgroup of $p $-power index? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.84.
Proposed by: A. L. Shmel'kin
Published resolution:
No, it is not (K. Seksenbaev, *Algebra i Logika*, **4**,
no. 3 (1965), 79--83 (Russian)). | 2 | solved | A. L. Shmel'kin | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No, it is not (K. Seksenbaev, *Algebra i Logika*, **4**,\nno. 3 (1965), 79--83 (Russian))."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,074 | KOU-1.85 | Kourovka Notebook Problem 1.85 | Is it true that the identity relations of a metabelian group
have a finite basis? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.85.
Proposed by: A. L. Shmel'kin
Published resolution:
Yes, it is (D. E. Cohen, *J. Algebra*, **5** (1967),
267--273). | 2 | solved | A. L. Shmel'kin | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it is (D. E. Cohen, *J. Algebra*, **5** (1967),\n267--273)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,075 | KOU-1.86 | Kourovka Notebook Problem 1.86 | Is it true that the identical relations of a
polycyclic group have a finite basis? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 1st issue (1965), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 1.86.
Proposed by: A. L. Shmel'kin | 2 | open | A. L. Shmel'kin | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,076 | KOU-1.87 | Kourovka Notebook Problem 1.87 | The same question for matrix groups (at least
over a field of characteristic 0). | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 1st issue (1965), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 1.87.
Proposed by: A. L. Shmel'kin | 2 | open | A. L. Shmel'kin | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,077 | KOU-1.88 | Kourovka Notebook Problem 1.88 | Is it true that if a matrix group over a field of
characteristic 0 does not satisfy any non-trivial identity
relation, then it contains a non-abelian free subgroup? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.88.
Proposed by: A. L. Shmel'kin
Published resolution:
Yes, it is (J. Tits, *J. Algebra*, **20** (1972),
250--270). | 2 | solved | A. L. Shmel'kin | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it is (J. Tits, *J. Algebra*, **20** (1972),\n250--270)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,078 | KOU-1.89 | Kourovka Notebook Problem 1.89 | Is the following assertion true? Let $G$ be a free soluble
group, and $a$ and $b$ elements of $G$ whose normal closures
coincide. Then there is an element $ x\in G$ such that $ b^{\pm
1} = x^{-1}ax$. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.89.
Proposed by: A. L. Shmel'kin
Published resolution:
No (A. L. Shmel'kin, *Algebra i Logika*, **6**, no. 2
(1967), 95--109 (Russian)). | 2 | solved | A. L. Shmel'kin | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No (A. L. Shmel'kin, *Algebra i Logika*, **6**, no. 2\n(1967), 95--109 (Russian))."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,079 | KOU-1.90 | Kourovka Notebook Problem 1.90 | A subgroup $H$ of a group $G$ is called *$2$-infinitely
isolated* in $G$ if, whenever the centralizer $C_G(h)$ in $G$
of some element $h\ne 1$ of $H$ contains at least one involution
and intersects $H$ in an infinite subgroup, it follows
that $C_G(h)\leq H$. Let $G$ be an infinite simple locally
finite group whose Sylo... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 1st issue (1965). Original problem number: 1.90.
Proposed by: V. P. Shunkov
Published resolution:
Yes, it does (V. P. Shunkov, *Algebra and Logic*, **11** (1972),
260--272). | 2 | solved | V. P. Shunkov | 1,965 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it does (V. P. Shunkov, *Algebra and Logic*, **11** (1972),\n260--272)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,080 | KOU-2.1 | Kourovka Notebook Problem 2.1 | Classify the finite groups having a Sylow $p $-subgroup as a
maximal subgroup. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.1.
Proposed by: V. A. Belonogov,
A. I. Starostin
Published resolution:
A description can be extracted from (B. Baumann, *J.
Algebra*, **38** (1976), 119--135) and (L. A. Shemetko... | 2 | solved | V. A. Belonogov,
A. I. Starostin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: A description can be extracted from (B. Baumann, *J.\nAlgebra*, **38** (1976), 119--135) and (L. A. Shemetkov, *Math. USSR--Izv.*, **2** (1968), 487--513)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,081 | KOU-2.2 | Kourovka Notebook Problem 2.2 | A *quasigroup* is a groupoid $Q(\cdot )$ in which the
equations $ ax = b$ and $ ya = b$ have a unique solution for any
$ a, b\in Q$. Two quasigroups $Q(\cdot )$ and $Q(\circ )$ are
*isotopic* if there are bijections $\alpha$, $\beta$,
$\gamma$ of the set $Q$ onto itself such that $x \circ y=\gamma
(\alpha x\cdot \beta ... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.2.
Proposed by: V. D. Belousov, A. A. Gvaramiya
Published resolution:
Every part is answered (A. A. Gvaramiya, Dep. no. 6704-V84,
VINITI, Moscow, 1984 (Russian)). | 2 | solved | V. D. Belousov, A. A. Gvaramiya | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Every part is answered (A. A. Gvaramiya, Dep. no. 6704-V84,\nVINITI, Moscow, 1984 (Russian))."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,082 | KOU-2.3 | Kourovka Notebook Problem 2.3 | A finite group is called *quasi-nilpotent* ($\Gamma$-*quasi-nilpotent*) if any two of its (maximal) subgroups $A$ and
$B$ satisfy one of the conditions 1) $ A \leq B$, \ \ 2) $ B \leq
A$, \ \ 3) $N_A(A\cap B) \ne A\cap B \ne N_B(A\cap B)$. Do the
classes of quasi-nilpotent and $\Gamma$-quasi-nilpotent groups
coincide? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.3.
Proposed by: Ya. G. Berkovich, M. I. Kravchuk
Published resolution:
No. The group $G=\left< x,y,z,t\mid
x^4=y^4=z^2=t^3=1,\;\;[x,y]=z,\;\; [x,z]=[y,z]=1,\right.$ $\left.
x^t=y... | 2 | solved | Ya. G. Berkovich, M. I. Kravchuk | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No. The group $G=\\left< x,y,z,t\\mid\nx^4=y^4=z^2=t^3=1,\\;\\;[x,y]=z,\\;\\; [x,z]=[y,z]=1,\\right.$ $\\left.\nx^t=y,\\;\\; y^t=x^{-1}y^{-1}\\right>$ is $\\Gamm... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,083 | KOU-2.4 | Kourovka Notebook Problem 2.4 | (S. Chase). Suppose that an abelian group $A$ can be written as
the union of pure subgroups $A_{\alpha}$, $\alpha\in\Omega$,
where $\Omega$ is the first non-denumerable ordinal,
$A_{\alpha}$ is a free abelian group of denumerable rank, and,
if $ \beta < \alpha$, then $A_{\beta}$ is a direct summand of $
A_{\alpha}$. Do... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.4.
Proposed by: Yu. A. Bogan
Published resolution:
Not always (P. A. Griffith, *Pacific J. Math.*, **29** (1969),
279--284). | 2 | solved | Yu. A. Bogan | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always (P. A. Griffith, *Pacific J. Math.*, **29** (1969),\n279--284)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,084 | KOU-2.5 | Kourovka Notebook Problem 2.5 | According to Plotkin, a group is called an $NR$-group if the set of its nil-elements coincides with the locally nilpotent radical, or, which is equivalent, if every inner automorphism of it is locally stable. Can an $NR$-group have a nil-automorphism that is not locally stable? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.5.
Proposed by: V. G. Vilyatser | 2 | open | V. G. Vilyatser | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,085 | KOU-2.6 | Kourovka Notebook Problem 2.6 | In an $NR$-group, the set of generalized central elements coincides with the nil-kernel. Is the converse true, that is, must a group be an $NR$-group if the set of generalized central elements coincides with the nil-kernel? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.6.
Proposed by: V. G. Vilyatser | 2 | open | V. G. Vilyatser | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,086 | KOU-2.7 | Kourovka Notebook Problem 2.7 | Find the cardinality of the set of all polyverbal operations
acting on the class of all groups. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.7.
Proposed by: O. N. Golovin
Published resolution:
It has the cardinality of the continuum (A. Yu. Olshanskii,
*Math. USSR--Izv.*, **4** (1970), 381--389). | 2 | solved | O. N. Golovin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: It has the cardinality of the continuum (A. Yu. Olshanskii,\n*Math. USSR--Izv.*, **4** (1970), 381--389)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,087 | KOU-2.8 | Kourovka Notebook Problem 2.8 | (A. I. Mal'cev). Do there exist regular
associative operations having the heredity property with respect
to transition from the factors to their subgroups? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.8.
Proposed by: O. N. Golovin
Published resolution:
Yes, there do (S. V. Ivanov, *Trans. Moscow Math. Soc.*, **1993**, 217--249). | 2 | solved | O. N. Golovin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, there do (S. V. Ivanov, *Trans. Moscow Math. Soc.*, **1993**, 217--249)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,088 | KOU-2.9 | Kourovka Notebook Problem 2.9 | Do there exist regular associative operations on the
class of groups satisfying the weakened Mal'cev condition (that is,
monomorphisms of the factors of an arbitrary product can be glued together, generally
speaking, into a homomorphism of the whole
product), but not satisfying the analogous condition for
epimorphisms ... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.9.
Proposed by: O. N. Golovin | 2 | open | O. N. Golovin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,089 | KOU-2.10 | Kourovka Notebook Problem 2.10 | Prove an analogue of the Remak--Shmidt theorem for decompositions of a group into nilpotent products. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.10.
Proposed by: O. N. Golovin
Published resolution:
Such an analogue is proved (V. V. Limanskiĭ, *Trudy Moskov. Mat. Obshch.*, **39** (1979), 135--155 (Russian)). | 2 | solved | O. N. Golovin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Such an analogue is proved (V. V. Limanskiĭ, *Trudy Moskov. Mat. Obshch.*, **39** (1979), 135--155 (Russian))."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,090 | KOU-2.13 | Kourovka Notebook Problem 2.13 | (Well-known problem). Let $G$ be a periodic group in which
every $\pi$-element commutes with every $\pi '$-element. Does
$G$ decompose into the direct product of a maximal
$\pi$-subgroup and a maximal $\pi '$-subgroup? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.13.
Proposed by: S. G. Ivanov
Published resolution:
Not always. S. I. Adian (*Math.
USSR--Izv.*, **5**
(1971), 475--484) has
constructed a group $A=A(m,n)$
which is torsion-free ... | 2 | solved | S. G. Ivanov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always. S. I. Adian (*Math.\nUSSR--Izv.*, **5**\n(1971), 475--484) has\nconstructed a group $A=A(m,n)$\nwhich is torsion-free and has a central element $d$ s... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,091 | KOU-2.15 | Kourovka Notebook Problem 2.15 | Does there exist a torsion-free group such that the factor
group by some term of its upper central series is nontrivial
periodic, with a bound on the orders of the elements? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.15.
Proposed by: G. A. Karas\"ev
Published resolution:
Yes, such groups do exist (S. I. Adian, *Proc. Steklov Inst. Math.*, **112**
(1971),
61--69). | 2 | solved | G. A. Karas\"ev | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, such groups do exist (S. I. Adian, *Proc. Steklov Inst. Math.*, **112**\n(1971),\n61--69)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,092 | KOU-2.16 | Kourovka Notebook Problem 2.16 | A group $G$ is called *conjugacy separable* if any two of
its elements are conjugate in $G$ if
and only if their images are conjugate in every finite
homomorphic image of $G$. Is $G$ conjugacy separable in the
following
cases:
a) $G$ is a polycyclic group,
b) $G$ is a free soluble group,
c) $G$ is a group of (all) i... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.16.
Proposed by: M. I. Kargapolov
Published resolution:
a) Yes (V. N. Remeslennikov, *Algebra and Logic*, **8**
(1969), 404--411); \ E. Formanek, *J. Algebra*, **42**
(1976), 1--... | 2 | solved | M. I. Kargapolov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: a) Yes (V. N. Remeslennikov, *Algebra and Logic*, **8**\n(1969), 404--411); \\ E. Formanek, *J. Algebra*, **42**\n(1976), 1--10).\n\nb) Yes (V. N. Remeslennikov,... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,093 | KOU-2.17 | Kourovka Notebook Problem 2.17 | Is it true that the wreath product $A\wr B$ of two groups
that are conjugacy separable is itself conjugacy separable if and
only if either $A$ is abelian or $B$ is finite? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.17.
Proposed by: M. I. Kargapolov
Published resolution:
No (V. N. Remeslennikov, *Siberian Math. J.*, **12**
(1971), 783--792). | 2 | solved | M. I. Kargapolov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No (V. N. Remeslennikov, *Siberian Math. J.*, **12**\n(1971), 783--792)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,094 | KOU-2.18 | Kourovka Notebook Problem 2.18 | Compute the ranks of the factors of the lower central series of
a free soluble group. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.18.
Proposed by: M. I. Kargapolov
Published resolution:
They were computed (V. G. Sokolov, *Algebra and Logic*,
**8** (1969),
212--215; \ Yu. M. Gorchakov, G. P. Egorychev, *Sovi... | 2 | solved | M. I. Kargapolov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: They were computed (V. G. Sokolov, *Algebra and Logic*,\n**8** (1969),\n212--215; \\ Yu. M. Gorchakov, G. P. Egorychev, *Soviet\nMath. Dokl.*, **13** (1972), 565... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,095 | KOU-2.19 | Kourovka Notebook Problem 2.19 | Are finitely generated subgroups of a free soluble group
finitely separable? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.19.
Proposed by: M. I. Kargapolov
Published resolution:
Not always (S. A. Agalakov, *Algebra and Logic*, **22** (1983),
261--268). | 2 | solved | M. I. Kargapolov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always (S. A. Agalakov, *Algebra and Logic*, **22** (1983),\n261--268)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,096 | KOU-2.20 | Kourovka Notebook Problem 2.20 | Is it true that the wreath products $A\wr B$ and $A_1\wr B_1$
are elementarily equivalent if and only if $A$, $B$ are
elementarily equivalent to $A_1$, $B_1$, respectively? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.20.
Proposed by: M. I. Kargapolov
Published resolution:
No, but if the word ``elementarily" is replaced by the word
``universally," then it is true (E. I. Timoshenko, *Algebra
an... | 2 | solved | M. I. Kargapolov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No, but if the word ``elementarily\" is replaced by the word\n``universally,\" then it is true (E. I. Timoshenko, *Algebra\nand Logic*, **7**, no. 4 (1968), 273-... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,097 | KOU-2.21 | Kourovka Notebook Problem 2.21 | Do the classes of Baer and Fitting groups coincide? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.21.
Proposed by: Sh. S. Kemkhadze
Published resolution:
No (R. S. Dark, *Math. Z.*, **105** (1968), 294--298). | 2 | solved | Sh. S. Kemkhadze | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No (R. S. Dark, *Math. Z.*, **105** (1968), 294--298)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,098 | KOU-2.22 | Kourovka Notebook Problem 2.22 | a) An abstract group-theoretic property $\Sigma$ is
said to be *radical $($in our sense*) if, in any group $G$,
the subgroup $\Sigma(G)$ generated by all normal $\Sigma
$-subgroups is a $\Sigma $-subgroup itself (called the *$\Sigma $-radical* of $G$). A radical property $\Sigma$ is said
to be *strongly radical* if, fo... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), updated in 21st issue (2026, arXiv:1401.0300v48). Original problem number: 2.22.
Proposed by: Sh. S. Kemkhadze
Archive of Solved Problems entry:
No. The group $SL_n(\mathbb{Z} )$ for sufficiently large $n\geq 3$ contains a
non-abelia... | 2 | partially_solved | Sh. S. Kemkhadze | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "partially_solved",
"checked_at": "2026-10-16",
"notes": "Part(s) solved in Archive of Solved Problems (No. The group $SL_n(\\mathbb{Z} )$ for sufficiently large $n\\geq 3$ contains a\nnon-abelian finite simple group and therefore is not an $N^0$-group.\nOn the oth... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,099 | KOU-2.23 | Kourovka Notebook Problem 2.23 | a) A subgroup $H$ of a group $G$ is called *quasisubinvariant* if there is a normal system of $G$ passing
through $H$. Let ${\mathfrak{K}}$ be a class of groups that is closed
with respect to taking homomorphic images. A group $G$ is called
an {\it $R^0({\mathfrak{K}})$-group} if each of its non-trivial
homomorphic ima... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.23.
Proposed by: Sh. S. Kemkhadze
Published resolution:
No, they do not (J. S. Wilson, *Arch. Math.*, **25** (1974), 574--577). | 2 | solved | Sh. S. Kemkhadze | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No, they do not (J. S. Wilson, *Arch. Math.*, **25** (1974), 574--577)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,100 | KOU-2.24 | Kourovka Notebook Problem 2.24 | Are Engel torsion-free groups orderable? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.24.
Proposed by: A. I. Kokorin | 2 | open | A. I. Kokorin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,101 | KOU-2.25 | Kourovka Notebook Problem 2.25 | a) (L. Fuchs). Describe the groups which are
linearly orderable in only finitely many ways.
[Archived solved part(s) of 2.25:]
b) Do there exist groups that are linearly orderable in
countably many ways? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), updated in 21st issue (2026, arXiv:1401.0300v48). Original problem number: 2.25.
Proposed by: A. I. Kokorin
Archive of Solved Problems entry:
Yes, there do (R. N. Buttsworth, *Bull. Austral. Math. Soc.*,
**4**
(1971), 97--104). | 2 | partially_solved | A. I. Kokorin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "partially_solved",
"checked_at": "2026-10-16",
"notes": "Part(s) solved in Archive of Solved Problems (Yes, there do (R. N. Buttsworth, *Bull. Austral. Math. Soc.*,\n**4**\n(1971), 97--104).); remaining part(s) in main section."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,102 | KOU-2.26 | Kourovka Notebook Problem 2.26 | (L. Fuchs). Characterize as abstract groups the
multiplicative groups of orderable skew fields. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.26.
Proposed by: A. I. Kokorin | 2 | open | A. I. Kokorin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,103 | KOU-2.28 | Kourovka Notebook Problem 2.28 | Can every orderable group be embedded in a
pro-orderable group? (See 1.35 for the definition of pro-orderable
groups.) | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.28.
Proposed by: A. I. Kokorin | 2 | open | A. I. Kokorin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,104 | KOU-2.29 | Kourovka Notebook Problem 2.29 | Does the class of finite groups in which every proper abelian
subgroup is contained in a proper normal subgroup coincide with
the class of finite groups in which every proper abelian subgroup
is contained in a proper normal subgroup of prime index? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.29.
Proposed by: P. G. Kontorovich, V. T. Nagrebetski\u{\i
Published resolution:
No. Let $B$ be a finite group such that $B=[B,B]\ne 1$ and let $r$
be the rank of $B$. Put $ A=\b... | 2 | solved | P. G. Kontorovich, V. T. Nagrebetski\u{\i | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No. Let $B$ be a finite group such that $B=[B,B]\\ne 1$ and let $r$\nbe the rank of $B$. Put $ A=\\bigoplus\\limits_{p\\mid |B|}(\\mathbb{Z} /p\\mathbb{Z} )\n^{r... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,105 | KOU-2.30 | Kourovka Notebook Problem 2.30 | Does there exist a finite group in which a Sylow $p $-subgroup
is covered by other Sylow $p $-subgroups? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.30.
Proposed by: P. G. Kontorovich, A. L. Starostin
Published resolution:
Yes, there does, for any prime $p$ \ (V. D. Mazurov, *Ural
Gos. Univ. Mat. Zap.*, **7**, no. 3 (1969/70)... | 2 | solved | P. G. Kontorovich, A. L. Starostin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, there does, for any prime $p$ \\ (V. D. Mazurov, *Ural\nGos. Univ. Mat. Zap.*, **7**, no. 3 (1969/70), 129--132\n(Russian))."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,106 | KOU-2.31 | Kourovka Notebook Problem 2.31 | Can every group admitting an ordering with only finitely many
convex subgroups be represented by matrices over a field? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.31.
Proposed by: V. M. Kopytov
Published resolution:
No, not every. For example, the group
$G=\left< a_n, b_n\;(n\in \mathbb{Z}
),\;c, d\mid [a_n,b_n]=c ,\right.$ $\left. a_n^d=a... | 2 | solved | V. M. Kopytov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No, not every. For example, the group\n$G=\\left< a_n, b_n\\;(n\\in \\mathbb{Z}\n),\\;c, d\\mid [a_n,b_n]=c ,\\right.$ $\\left. a_n^d=a_{n+1},\\;\\;\nb_n^d=b_{n+... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,107 | KOU-2.33 | Kourovka Notebook Problem 2.33 | Is a direct summand of a direct sum of finitely generated
modules over a Noetherian ring again a direct sum of finitely
generated modules? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.33.
Proposed by: V. I. Kuz'minov
Published resolution:
Not always (P. A. Linnell, *Bull. London Math. Soc.*, **14**
(1982),
124--126). | 2 | solved | V. I. Kuz'minov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always (P. A. Linnell, *Bull. London Math. Soc.*, **14**\n(1982),\n124--126)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,108 | KOU-2.35 | Kourovka Notebook Problem 2.35 | An inverse spectrum $\xi$ of abelian groups is
said to be *acyclic* if ${\lim\limits_{\longleftarrow}} ^{(p)}
\xi =0$ for $p > 0$. Here ${\lim\limits_{\longleftarrow}}^{(p)}$
denotes the right derived functor of the projective limit functor.
Let $\xi$ be an acyclic spectrum of finitely generated groups. Is
the spectrum... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.35.
Proposed by: V. I. Kuz'minov
Published resolution:
The answer depends on the axioms of Set Theory (A. A. Khusainov,
*Siberian Math. J.*, **37**, no. 2 (1996), 405--413). | 2 | solved | V. I. Kuz'minov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: The answer depends on the axioms of Set Theory (A. A. Khusainov,\n*Siberian Math. J.*, **37**, no. 2 (1996), 405--413)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,109 | KOU-2.36 | Kourovka Notebook Problem 2.36 | (de Groot). Is the group of all continuous integer-valued functions
on a compact space free abelian? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.36.
Proposed by: V. I. Kuz'minov
Published resolution:
Yes, it is. By (G. N\"obeling, *Invent. Math.*, **6**
(1968) 41--55) the additive group of all bounded
integer-valued funct... | 2 | solved | V. I. Kuz'minov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it is. By (G. N\\\"obeling, *Invent. Math.*, **6**\n(1968) 41--55) the additive group of all bounded\ninteger-valued functions\non an arbitrary set is free.... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,110 | KOU-2.37 | Kourovka Notebook Problem 2.37 | Describe the finite simple groups whose Sylow $p $-subgroups
are cyclic for all odd $p$. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.37.
Proposed by: V. D. Mazurov
Published resolution:
This was done (M. Aschbacher, *J. Algebra*, **54** (1978),
50--152). | 2 | solved | V. D. Mazurov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: This was done (M. Aschbacher, *J. Algebra*, **54** (1978),\n50--152)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,111 | KOU-2.38 | Kourovka Notebook Problem 2.38 | (Old problem). The class of rings embeddable in associative
division rings is universally axiomatizable. Is it finitely
axiomatizable? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.38.
Proposed by: A. I. Mal'cev
Published resolution:
No (P. M. Cohn, *Bull. London Math. Soc.*, **6** (1974), 147--148). | 2 | solved | A. I. Mal'cev | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No (P. M. Cohn, *Bull. London Math. Soc.*, **6** (1974), 147--148)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,112 | KOU-2.39 | Kourovka Notebook Problem 2.39 | Does there exist a non-finitely-axiomatizable variety of
a) (H. Neumann) groups?
b) of associative rings (the
Specht problem)?
c) Lie rings? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.39.
Proposed by: A. I. Mal'cev
Published resolution:
a) Yes, there does (S. I. Adian, *Math. USSR--Izv.*, **4** (1970), 721--739; \ A. Yu. Ol'shanskiĭ, *Math.
USSR--Izv.*, **4** ... | 2 | solved | A. I. Mal'cev | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: a) Yes, there does (S. I. Adian, *Math. USSR--Izv.*, **4** (1970), 721--739; \\ A. Yu. Ol'shanskiĭ, *Math.\nUSSR--Izv.*, **4** (1970), 381--389).\n\nb) Yes, ther... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,113 | KOU-2.40 | Kourovka Notebook Problem 2.40 | c) The *$I $-theory* (*$Q
$-theory*) of a class ${\mathfrak{K}}$ of universal algebras is the
totality of all identities (quasi-identities) that are valid on
all algebras in ${\mathfrak{K}}$. Does there exist a finitely
axiomatizable variety
(3) of Lie rings
(i) whose $I $-theory is non-decidable?
*Remark:* it is no... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), updated in 21st issue (2026, arXiv:1401.0300v48). Original problem number: 2.40.
Proposed by: A. I. Mal'cev
Archive of Solved Problems entry:
a) Yes (Yu. G. Kleiman, *Trans. Moscow Math. Soc.*, **1983**, no. 2, 63--110).
b) Yes (V. ... | 2 | partially_solved | A. I. Mal'cev | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "partially_solved",
"checked_at": "2026-10-16",
"notes": "Part(s) solved in Archive of Solved Problems (a) Yes (Yu. G. Kleiman, *Trans. Moscow Math. Soc.*, **1983**, no. 2, 63--110).\n\nb) Yes (V. L. Murskiĭ, *Math. Notes*, **3** (1968), 423--427).\n\nc) (1) Yes (V... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,114 | KOU-2.41 | Kourovka Notebook Problem 2.41 | Is the variety generated
by \
a) a finite associative ring;
b) a finite Lie ring;
c) a finite quasigroup
finitely axiomatizable?
d) What is the cardinality $n$ of the smallest semigroup
generating a non-finitely-axiomatizable variety? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.41.
Proposed by: A. I. Mal'cev
Published resolution:
a) Yes (I. V. L'vov, *Algebra and Logic*, **12** (1973),
156--167; \ R. L. Kruse, *J. Algebra*, **26** (1973), 298--318).
b)... | 2 | solved | A. I. Mal'cev | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: a) Yes (I. V. L'vov, *Algebra and Logic*, **12** (1973),\n156--167; \\ R. L. Kruse, *J. Algebra*, **26** (1973), 298--318).\n\nb) Yes (Yu. A. Bakhturin,\nA. Yu. ... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,115 | KOU-2.42 | Kourovka Notebook Problem 2.42 | What is the structure of the groupoid of
quasivarieties
a) of all semigroups?
b) of all rings?
c) of all associative rings?
Compare with A. I. Mal'cev, *Siberian
Math. J.*, **8**, no. 2 (1967), 254--267). | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.42.
Proposed by: A. I. Mal'cev | 2 | open | A. I. Mal'cev | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,116 | KOU-2.43 | Kourovka Notebook Problem 2.43 | A group $G$ is called an *$FN$-group* if the groups $\gamma_ iG/\gamma _{i+1}G$ are free
abelian and $\bigcap_{i=1}^{\infty} \gamma _iG = 1$, where $\gamma
_{i+1}G=[\gamma _{i}G, G]$. A variety of groups ${\mathfrak{M}}$ is
called a *$\Sigma$-variety* (where $\Sigma$ is an abstract
property) if the ${\mathfrak{M}}$-fre... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.43.
Proposed by: A. I. Mal'cev
Published resolution:
a) The property $FN$ is preserved by multiplication of varieties
(A. L. Shmel'kin, *Trans. Moscow Math. Soc.*, **29**
(1973),... | 2 | solved | A. I. Mal'cev | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: a) The property $FN$ is preserved by multiplication of varieties\n(A. L. Shmel'kin, *Trans. Moscow Math. Soc.*, **29**\n(1973), 239--252). The property $FN$ is n... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,117 | KOU-2.44 | Kourovka Notebook Problem 2.44 | Let ${\mathfrak{A}}$ and ${\mathfrak{B}}$ be subvarieties of a variety of
groups $
{\mathfrak{M}}$; then $({\mathfrak{A}}{\mathfrak{B}})\cap {\mathfrak{M}}$ is
called the {\it ${\mathfrak{M}}$-product of ${\mathfrak{A}}$ by ${\mathfrak{B}}$}, where $ {\mathfrak{A}}{\mathfrak{B}}$ is the usual product. Does
there exist ... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.44.
Proposed by: A. I. Mal'cev
Published resolution:
Yes, there does; for example, $ {\mathfrak{M}}={\mathfrak{A}}_p{\mathfrak{A}}_p$,
where ${\mathfrak{A}}_p$ is the variety of ... | 2 | solved | A. I. Mal'cev | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, there does; for example, $ {\\mathfrak{M}}={\\mathfrak{A}}_p{\\mathfrak{A}}_p$,\nwhere ${\\mathfrak{A}}_p$ is the variety of all abelian groups of prime\nex... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,118 | KOU-2.45 | Kourovka Notebook Problem 2.45 | b)
(P. Hall). Prove or refute the following conjecture:
If the marginal subgroup $v^*G$ has finite index $m$ in $G$,
then the order of $vG$ is finite and divides a power of $m$.
*Editors' comment:* There are examples when $|vG|$ does not divide a power of $m$
(Yu. G. Kleiman, *Trans. Moscow Math. Soc.*, **1983**,
no. ... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), updated in 21st issue (2026, arXiv:1401.0300v48). Original problem number: 2.45.
Proposed by: Yu. I. Merzlyakov
Archive of Solved Problems entry:
These conjectures are refuted in:
a) (S. V. Ivanov, *Soviet Math. (Izv. VUZ)*, **33**,... | 2 | partially_solved | Yu. I. Merzlyakov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "partially_solved",
"checked_at": "2026-10-16",
"notes": "Part(s) solved in Archive of Solved Problems (These conjectures are refuted in:\n\na) (S. V. Ivanov, *Soviet Math. (Izv. VUZ)*, **33**, no. 6 (1989), 59--70;\n\nc) I. S. Ashmanov, A. Yu. Olshanskii,\n*Soviet... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,119 | KOU-2.46 | Kourovka Notebook Problem 2.46 | Find conditions under which a finitely-generated matrix group
is almost residually a finite $p $-group for some prime $p$. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.46.
Proposed by: Yu. I. Merzlyakov
Published resolution:
A finitely generated matrix group over a field of characteristic
zero has a subgroup of finite index which is residually ... | 2 | solved | Yu. I. Merzlyakov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: A finitely generated matrix group over a field of characteristic\nzero has a subgroup of finite index which is residually a finite\n$p $-group for almost all pri... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,120 | KOU-2.47 | Kourovka Notebook Problem 2.47 | In which abelian groups is the lattice of
all fully invariant subgroups a chain? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.47.
Proposed by: A. P. Mishina
Published resolution:
Such groups were characterized (M.-P. Brameret, *S\'eminaire
P. Dubreil, M.-L. Dubreil-Jacotin, L. Lesieur, et C. Pisot*,
**1... | 2 | solved | A. P. Mishina | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Such groups were characterized (M.-P. Brameret, *S\\'eminaire\nP. Dubreil, M.-L. Dubreil-Jacotin, L. Lesieur, et C. Pisot*,\n**16** (1962/63), no. 13, Paris, 196... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,121 | KOU-2.48 | Kourovka Notebook Problem 2.48 | (N. Aronszajn). Let $G$ be a connected topological
group locally satisfying some identical relation $f|_U= 1$, where $U$
is a neighborhood of the identity element of $G$. Is it then true
that $f|_G=1$? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.48.
Proposed by: V. P. Platonov
Discussion and literature:
[Solved] No, not necessarily: for any odd integer $n\geq 10^{10}$
there is a connected topological g... | 2 | solved | V. P. Platonov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "maintained_source",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Confirmed solved (*) by editors in Kourovka Notebook 21st Issue (Oct 2026, arXiv:1401.0300v48): [Solved] No, not necessarily: for any odd integer $n\\geq 10^{10}$\nthere is a connected topological group such t... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,122 | KOU-2.49 | Kourovka Notebook Problem 2.49 | (A. Selberg). Let $G$ be a connected semisimple linear Lie
group whose corresponding symmetric space has rank greater than
1, and let $\Gamma$ be an irreducible discrete subgroup of $G$
such that $ G/\Gamma$ has finite volume. Does it follow that
$\Gamma$ is an arithmetic subgroup? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.49.
Proposed by: V. P. Platonov
Published resolution:
Yes, it does (G. A. Margulis, *Functional Anal. Appl.*, **8** (1974), 258--259). | 2 | solved | V. P. Platonov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it does (G. A. Margulis, *Functional Anal. Appl.*, **8** (1974), 258--259)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,123 | KOU-2.50 | Kourovka Notebook Problem 2.50 | (A. Selberg). Let $\Gamma$ be an irreducible discrete subgroup
of a connected Lie group $G$ such that the factor space
$G/\Gamma$ is non-compact but has finite volume in the Haar
measure. Prove that $\Gamma$ contains a non-trivial unipotent
element. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.50.
Proposed by: V. P. Platonov
Published resolution:
This is proved (D. A. Kazhdan, G. A. Margulis, *Math. USSR--Sb.*, **4** (1968), 147--152). | 2 | solved | V. P. Platonov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: This is proved (D. A. Kazhdan, G. A. Margulis, *Math. USSR--Sb.*, **4** (1968), 147--152)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,124 | KOU-2.51 | Kourovka Notebook Problem 2.51 | (A. Borel, R. Steinberg). Let $G$ be a semisimple algebraic
group and $R_G$ the set of classes of conjugate unipotent
elements of $ G$. Is $R_G$ finite? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.51.
Proposed by: V. P. Platonov
Published resolution:
Yes, it is (G. Lusztig, *Invent. Math.*, **34** (1976), 201--213). | 2 | solved | V. P. Platonov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it is (G. Lusztig, *Invent. Math.*, **34** (1976), 201--213)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,125 | KOU-2.52 | Kourovka Notebook Problem 2.52 | (F. Bruhat, N. Iwahori, M. Matsumoto). Let $G$ be a
semisimple algebraic group over a locally compact, totally
disconnected field. Do the maximal compact subgroups of $G$ fall
into finitely many conjugacy classes? If so, estimate this
number. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.52.
Proposed by: V. P. Platonov
Published resolution:
Yes, they do, and a formula for this number is found (F. Bruhat,
J. Tits, *Publ. Math. IHES*, **41** (1972), 5--251). | 2 | solved | V. P. Platonov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, they do, and a formula for this number is found (F. Bruhat,\nJ. Tits, *Publ. Math. IHES*, **41** (1972), 5--251)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,126 | KOU-2.54 | Kourovka Notebook Problem 2.54 | Can $SL(n,k)$ have maximal subgroups that are not closed in the Zariski topology? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.54.
Proposed by: V. P. Platonov
Published resolution:
Yes, it can if $k$ is either $\mathbb{Q}$ or an algebraically closed field of characteristic zero (N. S. Romanovskiĭ, *Algeb... | 2 | solved | V. P. Platonov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it can if $k$ is either $\\mathbb{Q}$ or an algebraically closed field of characteristic zero (N. S. Romanovskiĭ, *Algebra i Logika*, **6**, no. 4 (1967), 7... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,127 | KOU-2.55 | Kourovka Notebook Problem 2.55 | b) Does $SL_n(\mathbb{Z} )$, $n\geq 2$, have maximal subgroups of infinite index? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.55.
Proposed by: V. P. Platonov
Published resolution:
Yes, it does (G. A. Margulis, G. A. Soifer, *Soviet Math.
Dokl.*, **18** (1977), 847--851). | 2 | solved | V. P. Platonov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it does (G. A. Margulis, G. A. Soifer, *Soviet Math.\nDokl.*, **18** (1977), 847--851)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,128 | KOU-2.56 | Kourovka Notebook Problem 2.56 | Classify up to isomorphism the abelian connected
algebraic unipotent linear groups over a field of positive
characteristic. This is not difficult in the case of a field of
characteristic zero. On the other hand, C. Chevalley has solved
the classification problem for such groups up to isogeny. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.56.
Proposed by: V. P. Platonov | 2 | open | V. P. Platonov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,129 | KOU-2.58 | Kourovka Notebook Problem 2.58 | Let $G$ be a vector space and $\Gamma$ a group of automorphisms
of $G$. $\Gamma$ is called *locally finitely stable* if,
for any finitely generated subgroup $\Delta$ of $\Gamma$, \ $G$
has a finite series stable relative to $\Delta$. If the
characteristic of the field is zero and $\Gamma$ is locally
finitely stable, th... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.58.
Proposed by: B. I. Plotkin
Published resolution:
No (L. A. Simonyan, *Siberian Math. J.*, **12** (1971),
602--606). | 2 | solved | B. I. Plotkin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No (L. A. Simonyan, *Siberian Math. J.*, **12** (1971),\n602--606)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,130 | KOU-2.59 | Kourovka Notebook Problem 2.59 | Let $\Gamma$ be any nilpotent group of class $ n-1$. Does $
\Gamma$ always admit a faithful representation as a group of
automorphisms of an abelian group with a series of length $n$
stable relative to $\Gamma$? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.59.
Proposed by: B. I. Plotkin
Published resolution:
Not always (E. Rips, *Israel J. Math.*, **12** (1972),
342--346). | 2 | solved | B. I. Plotkin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always (E. Rips, *Israel J. Math.*, **12** (1972),\n342--346)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,131 | KOU-2.61 | Kourovka Notebook Problem 2.61 | Let $\Gamma$ be a Noetherian group of
automorphisms of a vector space $G$ such that every element of
$\Gamma$ is unipotent. Is $\Gamma$ necessarily a stable group of
automorphisms? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.61.
Proposed by: B. I. Plotkin
Published resolution:
Not if the field has non-zero characteristic
(A. Yu. Olshanskii, *The geometry of defining relations
in groups*, Kluwer, Dord... | 2 | solved | B. I. Plotkin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not if the field has non-zero characteristic\n(A. Yu. Olshanskii, *The geometry of defining relations\nin groups*, Kluwer, Dordrecht, 1991). This is true for fie... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,132 | KOU-2.62 | Kourovka Notebook Problem 2.62 | If $G$ is a finite-dimensional vector space over a field and $
\Gamma$ is a group of automorphisms of $G$ in which every element is
stable, then the whole of $\Gamma$ is stable (E. Kolchin). Is
Kolchin's theorem true for spaces over skew fields? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.62.
Proposed by: B. I. Plotkin
Published resolution:
Yes, it is, if the characteristic of the skew field
is zero or sufficiently large compared to the
dimension of the space (H. ... | 2 | solved | B. I. Plotkin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it is, if the characteristic of the skew field\nis zero or sufficiently large compared to the\ndimension of the space (H. Y. Mochizuki, *Canad. Math. Bull.*... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,133 | KOU-2.63 | Kourovka Notebook Problem 2.63 | Let $G$ be a group of automorphisms of a vector space over a field of characteristic zero, and suppose that all elements of $G$ are unipotent, with uniformly bounded unipotency indices. Must such a group be locally finitely stable? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.63.
Proposed by: B. I. Plotkin
Published resolution:
Yes, it must, which follows from (H. Heineken, *Arch. Math. (Basel)*, **13** (1962), 29--37). Moreover,
such a group is even ... | 2 | solved | B. I. Plotkin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, it must, which follows from (H. Heineken, *Arch. Math. (Basel)*, **13** (1962), 29--37). Moreover,\nsuch a group is even finitely stable, as follows from (E... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,134 | KOU-2.64 | Kourovka Notebook Problem 2.64 | Does the set of nil-elements of a finite-dimensional linear
group coincide with its locally nilpotent radical? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.64.
Proposed by: B. I. Plotkin
Published resolution:
Not always. The non-nilpotent $3$-generator nilgroup of E. S. Golod
constructed by an algebra over $\mathbb{Q}$ is residually... | 2 | solved | B. I. Plotkin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always. The non-nilpotent $3$-generator nilgroup of E. S. Golod\nconstructed by an algebra over $\\mathbb{Q}$ is residually torsion-free\nnilpotent; hence it... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,135 | KOU-2.65 | Kourovka Notebook Problem 2.65 | Does the adjoint group of a radical ring (in the sense of
Jacobson) have a central series? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.65.
Proposed by: B. I. Plotkin
Published resolution:
Not always (O. M. Neroslavskiĭ, *Vesci Akad. Navuk
BSSR,
Ser. Fiz.-Mat. Navuk*, **1973**, No. 2, 5--10 (Russian)). | 2 | solved | B. I. Plotkin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always (O. M. Neroslavskiĭ, *Vesci Akad. Navuk\nBSSR,\nSer. Fiz.-Mat. Navuk*, **1973**, No. 2, 5--10 (Russian))."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,136 | KOU-2.66 | Kourovka Notebook Problem 2.66 | Is an $R$-group determined by its subgroup lattice?
Is every lattice isomorphism of $R$-groups induced by a group
isomorphism? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.66.
Proposed by: L. E. Sadovski\u{\i
Published resolution:
Not always, in both cases (A. Yu. Olshanskii, *C. R. Acad. Bulgare Sci.*, **32**, no. 9 (1979), 1165--1166). | 2 | solved | L. E. Sadovski\u{\i | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always, in both cases (A. Yu. Olshanskii, *C. R. Acad. Bulgare Sci.*, **32**, no. 9 (1979), 1165--1166)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,137 | KOU-2.67 | Kourovka Notebook Problem 2.67 | Find conditions which ensure that the nilpotent
product of pure nilpotent groups (from certain classes) is
determined by the lattice of its subgroups. This is known to be
true if the product is torsion-free. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.67.
Proposed by: L. E. Sadovski\u{\i | 2 | open | L. E. Sadovski\u{\i | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,138 | KOU-2.68 | Kourovka Notebook Problem 2.68 | What can one say about lattice isomorphisms of a
pure soluble group? Is such a group strictly determined by its
lattice? It is well-known that the answer is affirmative for free
soluble groups. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.68.
Proposed by: L. E. Sadovski\u{\i | 2 | open | L. E. Sadovski\u{\i | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,139 | KOU-2.69 | Kourovka Notebook Problem 2.69 | Let a group $G$ be the product of two subgroups $A$ and $B$,
each of which is nilpotent and satisfies the minimum condition.
Prove or refute the following: \ a) $G$ is soluble; \ b) the
divisible parts of $A$ and $B$ commute elementwise. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.69.
Proposed by: N. F. Sesekin
Published resolution:
Both parts are proved (N. S. Chernikov, *Soviet Math.
Dokl.*, **21** (1980), 701--703). | 2 | solved | N. F. Sesekin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Both parts are proved (N. S. Chernikov, *Soviet Math.\nDokl.*, **21** (1980), 701--703)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,140 | KOU-2.70 | Kourovka Notebook Problem 2.70 | a) Let a group $G$ be the product of two subgroups $A$ and $B$,
each of which is locally cyclic and torsion-free. Prove that
either $A$ or $B$ has a non-trivial subgroup that is normal in
$G$.
b) Characterize the groups that can be factorized in this way. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.70.
Proposed by: N. F. Sesekin
Published resolution:
a) This was proved (D. I. Zaitsev, *Algebra and Logic*,
**19** (1980), 94--106).
b) They were characterized (Ya. P. Sysak, *... | 2 | solved | N. F. Sesekin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: a) This was proved (D. I. Zaitsev, *Algebra and Logic*,\n**19** (1980), 94--106).\n\nb) They were characterized (Ya. P. Sysak, *Algebra and Logic*, **25** (1986)... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,141 | KOU-2.71 | Kourovka Notebook Problem 2.71 | Does there exist a finitely generated
right-orderable group which coincides with its derived subgroup
and, therefore, does not have the property $RN$? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.71.
Proposed by: D. M. Smirnov
Published resolution:
Yes, there does (G. M. Bergman, *Pacific J. Math.*, **147**, no. 2 (1991), 243--248). | 2 | solved | D. M. Smirnov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, there does (G. M. Bergman, *Pacific J. Math.*, **147**, no. 2 (1991), 243--248)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,142 | KOU-2.72 | Kourovka Notebook Problem 2.72 | (G. Baumslag).
Suppose that $F$ is a finitely generated free group, $N$ its normal
subgroup and $V$ a fully invariant subgroup of $N$. Is $F/V$
necessarily Hopfian if $F/N$ is Hopfian? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.72.
Proposed by: D. M. Smirnov
Published resolution:
No, not necessarily
(S. V. Ivanov, A. M. Storozhev, *Geom. Dedicata*, **
114** (2005), 209--228). | 2 | solved | D. M. Smirnov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: No, not necessarily\n(S. V. Ivanov, A. M. Storozhev, *Geom. Dedicata*, **\n114** (2005), 209--228)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,143 | KOU-2.73 | Kourovka Notebook Problem 2.73 | (Well-known problem). Does there exist an
infinite group all of whose proper subgroups have prime order? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.73.
Proposed by: A. I. Starostin
Published resolution:
Yes, there does (A. Yu. Olshanskii, *Algebra and Logic*,
**21** (1982), 369--418). | 2 | solved | A. I. Starostin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, there does (A. Yu. Olshanskii, *Algebra and Logic*,\n**21** (1982), 369--418)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,144 | KOU-2.74 | Kourovka Notebook Problem 2.74 | (Well-known problem). Describe the finite groups
all of whose involutions have soluble centralizers. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.74.
Proposed by: A. I. Starostin | 2 | open | A. I. Starostin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,145 | KOU-2.75 | Kourovka Notebook Problem 2.75 | Let $G$ be a periodic group containing an infinite family of
finite subgroups whose intersection contains non-trivial
elements. Does $G$ contain a non-trivial element with infinite
centralizer? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.75.
Proposed by: S. P. Strunkov
Published resolution:
Not always (K. I. Lossov, Dep. no. 5528-V88, VINITI, Moscow,
1988 (Russian)). | 2 | solved | S. P. Strunkov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always (K. I. Lossov, Dep. no. 5528-V88, VINITI, Moscow,\n1988 (Russian))."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,146 | KOU-2.76 | Kourovka Notebook Problem 2.76 | Let $\Gamma$ be the holomorph of an abelian group $A$. Find
conditions for $A$ to be maximal among the locally nilpotent
subgroups of $\Gamma$. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.76.
Proposed by: D. A. Suprunenko
Published resolution:
These are found (A. V. Yagzhev, *Mat. Zametki*, **46**,
no. 6 (1989), 118 (Russian)). | 2 | solved | D. A. Suprunenko | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: These are found (A. V. Yagzhev, *Mat. Zametki*, **46**,\nno. 6 (1989), 118 (Russian))."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,147 | KOU-2.77 | Kourovka Notebook Problem 2.77 | Let $A$ and $B$ be abelian groups. Find conditions under which
every extension of $A$ by $B$ is nilpotent. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.77.
Proposed by: D. A. Suprunenko
Published resolution:
These are found (A. V. Yagzhev, *Math. Notes*, **43** (1988), 244--245). | 2 | solved | D. A. Suprunenko | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: These are found (A. V. Yagzhev, *Math. Notes*, **43** (1988), 244--245)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,148 | KOU-2.78 | Kourovka Notebook Problem 2.78 | Any set of all subgroups of the same given order of a finite group
$G$ that contains at least one non-normal subgroup
is called an $IE_{\bar n}$-system of $G$. A positive integer $k$
is called a
*soluble* (*non-soluble; \
simple; \
composite; \
absolutely simple*)
*group-theoretic number*
if every finite group having e... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.78.
Proposed by: P. I. Trofimov | 2 | open | P. I. Trofimov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,149 | KOU-2.79 | Kourovka Notebook Problem 2.79 | Do there exist divisible (simple) groups with maximal
subgroups? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.79.
Proposed by: M. S. Tsalenko
Published resolution:
Yes, there do (V. G. Sokolov, *Algebra
Logic*, **7** (1968), 122--126). | 2 | solved | M. S. Tsalenko | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Yes, there do (V. G. Sokolov, *Algebra\nLogic*, **7** (1968), 122--126)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,150 | KOU-2.80 | Kourovka Notebook Problem 2.80 | Does every non-trivial group satisfying the
normalizer condition contain a non-trivial abelian normal
subgroup? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.80.
Proposed by: S. N. Chernikov | 2 | open | S. N. Chernikov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,151 | KOU-2.81 | Kourovka Notebook Problem 2.81 | a) Does there exist an axiomatizable class of
lattices $ {\mathfrak{K}}$ such that the lattice of all subsemigroups
of a semigroup $S$ is isomorphic to some lattice in ${\mathfrak{K}}$ if
and only if $S$ is a free group?
b) The same question for free
abelian groups.
Analogous questions have affirmative answers for
to... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.81.
Proposed by: L. N. Shevrin
Discussion and literature:
[Solved] a), b) Yes, there are such classes (AI solution confirmed by O. G. Kharlampovich: \ Achyuth ... | 2 | solved | L. N. Shevrin | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "maintained_source",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Confirmed solved (*) by editors in Kourovka Notebook 21st Issue (Oct 2026, arXiv:1401.0300v48): [Solved] a), b) Yes, there are such classes (AI solution confirmed by O. G. Kharlampovich: \\ Achyuth Jayadevan, ... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,152 | KOU-2.82 | Kourovka Notebook Problem 2.82 | Can the class of groups with the $n $th Engel condition
$[x,\underbrace{y,\ldots ,y}_{n}]=1$ be defined by identical
relations of the form $u=v$, where $u$ and $v$ are words without
negative powers of variables? This can be done for $n=1, 2, 3$
(A. I. Shirshov, *Algebra i Logika*, **2**, no. 5 (1963),
5--18 (Russian)).... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 2nd issue (1967), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 2.82.
Proposed by: A. I. Shirshov | 2 | open | A. I. Shirshov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
700,153 | KOU-2.83 | Kourovka Notebook Problem 2.83 | Suppose that a periodic group $G$ is the
product of two locally finite subgroups. Is then $G$ locally
finite? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), Archive of Solved Problems, 2nd issue (1967). Original problem number: 2.83.
Proposed by: V. P. Shunkov
Published resolution:
Not always (V. I. Sushchanskiĭ, *Math. USSR--Sb.*, **67**, no. 2 (1990), 535--553). | 2 | solved | V. P. Shunkov | 1,967 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 10,
"name": "kourovka_new_problems_21",
"display_name": "Kourovka Notebook (Issues 1–21)",
"description": "Unsolved and archive-solved problems in group theory from Issues 1–21 (1965–2026) of the Kourovka Notebook, edited by E. I. Khukhro and V. D. Mazurov.",
"slug": "kourovka-new-problems-21",
"ord... | null | {
"evidence": "published",
"canonical_status": "solved",
"checked_at": "2026-10-16",
"notes": "Solved in Kourovka Notebook Archive of Solved Problems: Not always (V. I. Sushchanskiĭ, *Math. USSR--Sb.*, **67**, no. 2 (1990), 535--553)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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