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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
701,754 | KOU-20.96 | Kourovka Notebook Problem 20.96 | Is a periodic group a Frobenius group if it has a proper non-trivial normal abelian subgroup
that contains the centralizer of each of its non-identity elements? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.96.
Proposed by: A. I. Sozutov
Discussion and literature:
[Solved] Yes, it is (D. V. Lytkina, V. D. Mazurov, *Siberian Math. J.*, **64**, no. 6 (2023), 1350-... | 2 | solved | A. I. Sozutov | 2,022 | 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] Yes, it is (D. V. Lytkina, V. D. Mazurov, *Siberian Math. J.*, **64**, no. 6 (2023), 1350--1353)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
701,755 | KOU-20.97 | Kourovka Notebook Problem 20.97 | Is a 2-group locally finite if the centralizer of every involution is locally finite? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.97.
Proposed by: N. M. Suchkov | 2 | open | N. M. Suchkov | 2,022 | 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 |
701,756 | KOU-20.98 | Kourovka Notebook Problem 20.98 | Let $G$ be a group of permutations of the set of positive integers $\mathbb{N}$ isomorphic to the additive group of rational numbers. Must there be an element $g\in G$ such that the set $\{a-ag\mid a\in \mathbb{N}\}$ is infinite? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.98.
Proposed by: N. M. Suchkov
Discussion and literature:
[Solved] Yes, it must (N. M. Suchkov, A. A. Shlepkin, D. A. Taysnyov, *Siberian Math. J.*, **65** (... | 2 | solved | N. M. Suchkov | 2,022 | 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] Yes, it must (N. M. Suchkov, A. A. Shlepkin, D. A. Taysnyov, *Siberian Math. J.*, **65** (2024), 1390--1... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
701,757 | KOU-20.99 | Kourovka Notebook Problem 20.99 | *Conjecture*: Let $a_1G_1,\ldots,a_kG_k$, $k>1$, be finitely many pairwise disjoint left cosets in
a group $G$ with $[G:G_i]<\infty$ for all $i=1,\ldots,k$. Then
$\gcd([G:G_i],[G:G_j])\ge k\qquad \text{for some }1\leq i<j\leq k$.
The conjecture is known to hold for $k=2,3,4$. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.99.
Proposed by: Z.-W. Sun | 2 | open | Z.-W. Sun | 2,022 | 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 |
701,758 | KOU-20.100 | Kourovka Notebook Problem 20.100 | *Conjecture*:
Let $n$ be a positive integer, and let $G$ be a group
containing no elements of order among $2,\ldots,n+1$.
Then, for any $A\subseteq G$ with $|A|=n$, we may write $A=\{a_1,\ldots,a_n\}$
with $a_1,a_2^2,\ldots,a_n^n$ pairwise distinct.
The conjecture is known to hold for $n\leq 3$. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.100.
Proposed by: Z.-W. Sun | 2 | open | Z.-W. Sun | 2,022 | 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 |
701,759 | KOU-20.101 | Kourovka Notebook Problem 20.101 | Let $G$ be a finitely generated branch group. Are all finite-index maximal subgroups of $G$ necessarily normal?
Cf. 18.81. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.101.
Proposed by: A. Thillaisundaram
Discussion and literature:
[Solved] No, not necessarily (P. Neumann, *Illinois J. Math.*, **30** (1986), 301--316). More... | 2 | solved | A. Thillaisundaram | 2,022 | 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 (P. Neumann, *Illinois J. Math.*, **30** (1986), 301--316). Moreover, there are fini... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
701,760 | KOU-20.102 | Kourovka Notebook Problem 20.102 | (Y. Barnea, A. Shalev). Let $G$ be a finitely generated pro-$p$ group. Must $G$ be $p$-adic analytic if it has finite Hausdorff spectrum with respect to
a) the $p$-power series?
b) the iterated $p$-power series?
c) the lower $p$-series?
d) the Frattini series?
e) the dimension subgroup series? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.102.
Proposed by: A. Thillaisundaram | 2 | open | A. Thillaisundaram | 2,022 | 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 |
701,761 | KOU-20.103 | Kourovka Notebook Problem 20.103 | Let $G_\Gamma$ be a partially commutative soluble group
of derived length $n \geq 3$ with defining graph $\Gamma$ (the
definition is similar to the case of $n=2$, see 17.104). Is
$G_\Gamma$ a torsion-free group? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.103.
Proposed by: E. I. Timoshenko | 2 | open | E. I. Timoshenko | 2,022 | 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 |
701,762 | KOU-20.104 | Kourovka Notebook Problem 20.104 | (Well-known questions).
Suppose that a group $G$ is finitely generated and decomposable into a direct product $G = G_1 \times G_2$.
a) Is it true that the elementary theory of $G$ is decidable if and only if the elementary theories of the groups $G_1$ and $G_2$ are decidable?
b) Is it true that the universal theory o... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.104.
Proposed by: E. I. Timoshenko | 2 | open | E. I. Timoshenko | 2,022 | 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 |
701,763 | KOU-20.105 | Kourovka Notebook Problem 20.105 | Is there a perfect locally nilpotent $p$-group, for some prime $p$, whose proper subgroups are hypercentral? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.105.
Proposed by: N. Trabelsi | 2 | open | N. Trabelsi | 2,022 | 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 |
701,764 | KOU-20.106 | Kourovka Notebook Problem 20.106 | Let $G$ be a residually finite $2$-group and let $x\in G$ be a left 3-Engel element of order 2. Is $\langle x^{G}\rangle$ locally nilpotent?
It is known that in any group a 3-Engel element of odd order belongs to the locally nilpotent radical (E. Jabara, G. Traustason, *Proc. Amer. Math. Soc.*, **147**, no. 5 (2019), ... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.106.
Proposed by: G. Traustason | 2 | open | G. Traustason | 2,022 | 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 |
701,765 | KOU-20.107 | Kourovka Notebook Problem 20.107 | Let $G$ be a group of exponent 8 and $x\in G$ a left 3-Engel element of order 2. Is $\langle x^{G}\rangle$ locally finite? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.107.
Proposed by: G. Traustason | 2 | open | G. Traustason | 2,022 | 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 |
701,766 | KOU-20.108 | Kourovka Notebook Problem 20.108 | The *holomorph* $\mathrm{Hol}(G)$ of a group $G$ can be defined as the normalizer of the subgroup of left translations in the group of all permutations of the set $G$. The *multiple holomorph* $\mathrm{NHol}(G)$ of $G$ is the normalizer of the holomorph. Set $T(G) = \mathrm{NHol}(G)/\mathrm{Hol}(G)$.
a) Is there a cen... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.108.
Proposed by: C. Tsang
Discussion and literature:
[Solved] a), b) Yes, there is, in both cases (AI solution confirmed by C. Tsang: \ M. Kinyon, J. Urban,... | 2 | partially_solved | C. Tsang | 2,022 | 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": "partially_solved",
"checked_at": "2026-10-16",
"notes": "Subproblem confirmed solved (*) in Kourovka Notebook 21st Issue (Oct 2026, arXiv:1401.0300v48): [Solved] a), b) Yes, there is, in both cases (AI solution confirmed by C. Tsang: \\ M. Kinyon, J. Urban... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
701,767 | KOU-20.109 | Kourovka Notebook Problem 20.109 | A *skew brace* is a set $B$ equipped with two operations $+$ and $\cdot$ such that $(B,+)$ is an additively written (but not necessarily abelian) group, $(B,\cdot )$ is a multiplicatively written group, and $a\cdot (b+c)=ab-a+ac$ for any $a,b,c\in B$.
Is there a finite skew brace with perfect additive group and non-pe... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.109.
Proposed by: C. Tsang
Discussion and literature:
[Solved] Yes, there is (M. Di Matteo, M. Ferrara, *Preprint*, 2026, https://arxiv.org/abs/2607.14059 | 2 | solved | C. Tsang | 2,022 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
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} | {
"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",
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"checked_at": "2026-10-16",
"notes": "Confirmed solved (*) by editors in Kourovka Notebook 21st Issue (Oct 2026, arXiv:1401.0300v48): [Solved] Yes, there is (M. Di Matteo, M. Ferrara, *Preprint*, 2026, https://arxiv.org/abs/2607.14059"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
701,768 | KOU-20.110 | Kourovka Notebook Problem 20.110 | Are there residually finite hereditarily just infinite groups that are
a) amenable but not solvable?
b) amenable but not elementary amenable?
c) of intermediate word growth?
d) of intermediate subgroup growth?
All examples that we know are either linear (hence Tits Alternative applies), or have a quotient with pro... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.110.
Proposed by: M. Vannacci | 2 | open | M. Vannacci | 2,022 | 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 |
701,769 | KOU-20.111 | Kourovka Notebook Problem 20.111 | Are there residually finite hereditarily just infinite groups admitting a self-similar action on a rooted tree that are not linear? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.111.
Proposed by: M. Vannacci | 2 | open | M. Vannacci | 2,022 | 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 |
701,770 | KOU-20.112 | Kourovka Notebook Problem 20.112 | Let $\mathfrak{F}$ be a hereditary saturated formation and let $\mathrm{w}^{*}\mathfrak{F}$ denote the class of all
finite groups $G$ for which
$\pi(G)\subseteq\pi(\mathfrak{F})$ and the normalizers of all Sylow subgroups of $G$ are $\mathfrak{F}$-subnormal in $G$.
It is known that $\mathrm{w}^{*}\mathfrak{F}$ is a for... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.112.
Proposed by: A. F. Vasil'ev, T. I. Vasil'eva | 2 | open | A. F. Vasil'ev, T. I. Vasil'eva | 2,022 | 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 |
701,771 | KOU-20.113 | Kourovka Notebook Problem 20.113 | Let $H(q,c) = \langle a,b,c,d \mid [b,a]=[d,c], \text{ of exponent } q, \text{ nilpotent of class } c\rangle$.
a) Is it true that the Schur multiplier $M(H(8,12))$ has exponent 32?
b) Is it true that the Schur multiplier $M(H(7,13))$ has exponent 49?
The difficulty is that these groups are too big to compute using c... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.113.
Proposed by: M. R. Vaughan-Lee | 2 | open | M. R. Vaughan-Lee | 2,022 | 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 |
701,772 | KOU-20.114 | Kourovka Notebook Problem 20.114 | Is there a positive integer $c$ such that for any $q$ the exponent of the Schur multiplier of a finite group of exponent $q$ divides $q^c$? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.114.
Proposed by: M. R. Vaughan-Lee | 2 | open | M. R. Vaughan-Lee | 2,022 | 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 |
701,773 | KOU-20.115 | Kourovka Notebook Problem 20.115 | Let $\chi$ be a complex irreducible character of a finite group $G$. If $\chi(x)\ne 0$ for some $x\in G$, must the order $o(x)$ of $x$ divide $|G|/\chi(1)$?
This is known to be true if $G$ is solvable, and it is known that $(o(x)\chi(1))^4$ divides $|G|^5$ for arbitrary $G$. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.115.
Proposed by: T. Wilde | 2 | open | T. Wilde | 2,022 | 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 |
701,774 | KOU-20.116 | Kourovka Notebook Problem 20.116 | (Well-known problem).
Does a profinite torsion group have finite exponent?
This problem reduces to the case of pro-$p$ groups (cf. W. Herfort, *Arch. Math.*, **33** (1980), 404--410). Also cf. Archive 3.41. | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.116.
Proposed by: John S. Wilson | 2 | open | John S. Wilson | 2,022 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
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"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 |
701,775 | KOU-20.117 | Kourovka Notebook Problem 20.117 | Let $G$ be a pro-$p$ group that is a 3-dimensional Poincar\'e duality group. Is $G$ coherent?
A group is said to be *coherent* if each of its finitely generated subgroups is finitely presented, and in the question the coherency is used in the pro-$p$ sense. The question is a famous problem for abstract groups, but has... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.117.
Proposed by: P. Zalesskii | 2 | open | P. Zalesskii | 2,022 | 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 |
701,776 | KOU-20.118 | Kourovka Notebook Problem 20.118 | Let $G$ be a pro-$p$ group that is a 3-dimensional Poincar\'e duality group. Can it contain a direct product $F_2\times F_2$ of free pro-$p$ groups of rank 2?
If it can, then the answer to 20.117 is negative, but in the abstract case it is known that it can not (P. H. Kropholler, M. A. Roller, *J. London
Math. Soc. (2... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.118.
Proposed by: P. Zalesskii | 2 | open | P. Zalesskii | 2,022 | 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 |
701,777 | KOU-20.119 | Kourovka Notebook Problem 20.119 | (G. Wilkes).
A pro-$p$ group is said to be *accessible* if there is a
number $n = n(G)$ such that any finite proper reduced graph of pro-$p$ groups with finite edge groups having fundamental group isomorphic to $G$ has at most $n$ edges (*J. Algebra*, **525** (2019), 1--18).
Is every finitely presented pro-$p$ group a... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.119.
Proposed by: P. Zalesskii | 2 | open | P. Zalesskii | 2,022 | 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 |
701,778 | KOU-20.120 | Kourovka Notebook Problem 20.120 | Let $G$ be a locally nilpotent group with an automorphism (of infinite order). Can $G$ be simple as a group with automorphism? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.120.
Proposed by: E. I. Zelmanov | 2 | open | E. I. Zelmanov | 2,022 | 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 |
701,779 | KOU-20.121 | Kourovka Notebook Problem 20.121 | Let $G$ be a finite almost simple group such that $Soc(G)$ is a non-soluble group of Lie type over a field of characteristic $p$. Let $R$ be a Sylow $q$-subgroup of $G$ (for some $q$) and let $\operatorname{Min}_G(R)$ be the subgroup of $R$ generated by all minimal by inclusion intersections of the form $R\cap R^g$, wh... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.121.
Proposed by: V. I. Zenkov
Discussion and literature:
[Solved] Yes, it is true (T. C. Burness, H. Y. Huang, *Preprint*, 2025, https://arxiv.org/pdf/2506.... | 2 | solved | V. I. Zenkov | 2,022 | 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] Yes, it is true (T. C. Burness, H. Y. Huang, *Preprint*, 2025, https://arxiv.org/pdf/2506.19745)."
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
701,780 | KOU-20.122 | Kourovka Notebook Problem 20.122 | For nilpotent subgroups $A,B, C$ of a finite group $G$, let
$\operatorname{Min}_G(A,B,C)$ be the subgroup of $A$ generated by all minimal by inclusion
intersections of the form $A\cap B^x\cap C^y$, where $ x, y\in G$, and let $\operatorname{min}_G(A,B,C)$ be the subgroup of $\operatorname{Min}_G(A,B,C)$ generated by al... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.122.
Proposed by: V. I. Zenkov
Discussion and literature:
[Solved] a), b), c) No, it is not always true in all three cases (AI solution confirmed by V. I. Ze... | 2 | solved | V. I. Zenkov | 2,022 | 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",
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"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), c) No, it is not always true in all three cases (AI solution confirmed by V. I. Zenkov: \\ M. Ki... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
701,781 | KOU-20.123 | Kourovka Notebook Problem 20.123 | A finite group is called a {\it $D_{\pi} $-group} if any two of its maximal $\pi
$-subgroups
are conjugate.
a) Is it true that for any finite $D_\pi$-group $G$ and a $\pi$-Hall subgroup $H$ of $G$, there are elements $x,y,z\in G$ such that $O_{\pi }(G)=H\cap H^x\cap H^y\cap H^z$?
b)
Suppose that $G$ is a finite $D_{\... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.123.
Proposed by: V. I. Zenkov
Discussion and literature:
[Solved] b) Yes, it is true (I. N. Belousov, V. I. Zenkov, Preprint, 2025 (Russian),
https://kouro... | 2 | partially_solved | V. I. Zenkov | 2,022 | 17 | 10 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
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"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": "partially_solved",
"checked_at": "2026-10-16",
"notes": "Subproblem confirmed solved (*) in Kourovka Notebook 21st Issue (Oct 2026, arXiv:1401.0300v48): [Solved] b) Yes, it is true (I. N. Belousov, V. I. Zenkov, Preprint, 2025 (Russian),\n\nhttps://kourovk... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
701,782 | KOU-20.124 | Kourovka Notebook Problem 20.124 | A *Rota--Baxter operator* on a group $G$ is a mapping $B : G \to G$ such that
$B(g) B(h) = B\left(gB(g)hB(g)^{-1} \right)$ for all $g, h \in G$.
Let $F$ be a non-abelian free group. Is there a Rota--Baxter operator on $F$ such that its image is equal to the derived subgroup $[F, F]$? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.124.
Proposed by: V. G. Bardakov | 2 | open | V. G. Bardakov | 2,022 | 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 |
701,783 | KOU-20.125 | Kourovka Notebook Problem 20.125 | Does there exist a non-abelian group $G$ and a Rota--Baxter operator $B : G \to G$ such that $B$ is surjective but not injective? | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.125.
Proposed by: V. G. Bardakov
Discussion and literature:
[Solved] Yes, it does exist (AI solution confirmed by V. G. Bardakov: \ P. Monticone, *Preprint*,... | 2 | solved | V. G. Bardakov | 2,022 | 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] Yes, it does exist (AI solution confirmed by V. G. Bardakov: \\ P. Monticone, *Preprint*, 2026, https://... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
701,784 | KOU-20.126 | Kourovka Notebook Problem 20.126 | A *brace* $(G; +, \circ)$ is non-empty set $G$ with two binary operations $+$, $\circ$ such that
$(G, +)$ is an additively written abelian group, $(G, \circ)$ is a multiplicatively written group, and $a \circ (b + c) + a = (a \circ b) + (a \circ c)$ for all $a, b, c \in G$. Does there exist a brace with finitely genera... | Source: The Kourovka Notebook (Unsolved Problems in Group Theory), 20th issue (2022), 21st issue edition (2026, arXiv:1401.0300v48). Original problem number: 20.126.
Proposed by: V. G. Bardakov, M. V. Neshchadim, M. K. Yadav | 2 | open | V. G. Bardakov, M. V. Neshchadim, M. K. Yadav | 2,022 | 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 |
800,001 | AMR-113-0001 | The Lyapin's Notebook — Problem 1 | (S. Kublanovsky, M. Sapir)
Describe the types of equations or systems of equations for which there exists an algorithm that decides for any values of the constants whether the given system is solvable in some finite extension of the original semigroup. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 1
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,002 | AMR-113-0002 | The Lyapin's Notebook — Problem 2 | (S. Kublanovsky)
Describe the divisors of the following subclasses of finite 0-simple semigroups:
- the class of finite Brandt semigroups;
- the class of finite 0-simple semigroups presented in the Rees representation by a matrix that consists only of zeros and ones.
Divisors of the class of all finite 0-simple semi... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 2
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,003 | AMR-113-0003 | The Lyapin's Notebook — Problem 3 | (S. Bershadsky, S. Kublanovsky)
Is there an algorithm that decides whether a given finite semigroup is embeddable into a power semigroup over some finite group (periodic group) (see Chapter 5 of this notebook)?
Not every finite semigroup has this property, but every semigroup is a divisor of the power semigroup over a... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 3
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,004 | AMR-113-0004 | The Lyapin's Notebook — Problem 4 | (E.S. Lyapin)
Describe the identities of the full transformation semigroup $T(n)$ on an $n$-element set. \\
A description of some classes of identities was obtained in the works [PSSSV], [Ma3]. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 4
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,005 | AMR-113-0005 | The Lyapin's Notebook — Problem 5 | (S. Kublanovsky)
Describe locally residually finite varieties of semigroups for known predicates.\\
In the global case, such description is obtained in [Kubl1], [Kubl2]. For the equality predicate in the local case, the description is obtained in [Sapir]. Locally residually finite varieties of rings were described in [... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 5
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,006 | AMR-113-0006 | The Lyapin's Notebook — Problem 6 | (S. Kublanovsky)
Describe the covers of the semigroup variety $RS_n$ in the lattice of varieties of all semigroups and in the lattice of varieties satisfying the identity $x^2 = x^{n+2}$. \\
It follows from the results of [Kubl5] that in the latter lattice the number of covers is finite. It is also known that every sub... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 6
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,007 | AMR-113-0007 | The Lyapin's Notebook — Problem 7 | (S. Kublanovsky)
Describe periodic varieties generated by regular semigroups. \\
For periodic varieties generated by completely 0-simple semigroups, such a description was obtained in [Kubl4]. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 7
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,008 | AMR-113-0008 | The Lyapin's Notebook — Problem 8 | (I. Melnichuk)
Let $c(u)$ denote the number of distinct letters occuring in the word $u$. Let $m(u)$ denote the minimal number of letters in a finite alphabet $A$ for which there exists an infinite word over $A$ that does not contain images of $u$ under substitutions. Determine the number $m(u)$ for a non-blocking word... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 8
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,009 | AMR-113-0009 | The Lyapin's Notebook — Problem 9 | (G. Mashevitzky)
Is the set of finite finitely based completely 0-simple semigroups over Abelian groups, in particular, over a two-element group, recursive?\\
An infinite chain of varieties, generated by completely 0-simple semigroups over the two-element group, in which finitely based and non-finitely based varieties ... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 9
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,010 | AMR-113-0010 | The Lyapin's Notebook — Problem 10 | (E.S. Lyapin)
Under what conditions is a system of identical inequalities (identical relations of precedence) equivalent to a system of identities?\\
This problem is solved for systems consisting of a single identical inequality in [Mak1]. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 10
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,011 | AMR-113-0011 | The Lyapin's Notebook — Problem 11 | (E.S. Lyapin)
Describe all varieties of ordered semigroups that have covers in the lattice of varieties of ordered semigroups. \\
Some such varieties are described in works [Mak2], [Mak3]. In the lattice of varieties of ordered semigroups, not every variety has a cover (see [Mak2]). | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 11
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,012 | AMR-113-0012 | The Lyapin's Notebook — Problem 12 | (V. Makaridina)
Describe all varieties of ordered semigroups in which every semigroup has only the trivial order.\\
Some examples are given in [Mak4]. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 12
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,013 | AMR-113-0013 | The Lyapin's Notebook — Problem 13 | Let $K$ be a class of semigroups. For each natural number $n$, denote by $f_K(n)$ the minimal number of endomorphisms among all finite semigroups from $K$ having at least $n$ elements. The function $f_K(n)$ is called the *endomorphic function* of the class $K$. A class $K$ is called *endomorphic* if its endomorphic fun... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 13
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,014 | AMR-113-0014 | The Lyapin's Notebook — Problem 14 | (S. Kublanovsky)
Is it true that for every variety of commutative semigroups its endomorphic function is identical? \\
The variety of commutative semigroups is endomorphic (see [kubl]). | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 14
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,015 | AMR-113-0015 | The Lyapin's Notebook — Problem 15 | (S. Kublanovsky)
Is it true that for any endomorphic variety of semigroups its endomorphic function is identical? | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 15
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,016 | AMR-113-0016 | The Lyapin's Notebook — Problem 16 | (S. Kublanovsky)
Obtain estimates for the values of the endomorphic function for various basic classes of semigroups. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 16
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,017 | AMR-113-0017 | The Lyapin's Notebook — Problem 17 | (A.A. Borisov)
Describe finitely generated Lesokhin semigroups without idempotents.\\
It is proved in [Borisov4] that finitely generated separative Lesokhin semigroups without idempotents should be isomorphic to subsemigroups of an infinite monogenic semigroup. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 17
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,018 | AMR-113-0018 | The Lyapin's Notebook — Problem 18 | (A.A. Borisov)
Describe commutative semigroups all of whose endomorphisms are injective. \\
It is proved in [Borisov4] that finitely generated commutative semigroups all of whose endomorphisms are injective are precisely subsemigroups of an infinite monogenic semigroups or finite ordinal sums of such semigroups. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 18
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,019 | AMR-113-0019 | The Lyapin's Notebook — Problem 19 | (A.A. Borisov)
Describe finitely generated commutative separative E-semigroups. \\
It is proved in [Borisov4] that for a finitely defined commutative semigroup the problem of deciding whether
the semigroup of all its endomorphisms (under pointwise multiplication) is Archimedean is algorithmically solvable. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 19
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,020 | AMR-113-0020 | The Lyapin's Notebook — Problem 20 | (A.A. Borisov)
Describe commutative semigroups whose semigroups of endomorphisms (with pointwise multiplication) is cancelative. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 20
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,021 | AMR-113-0021 | The Lyapin's Notebook — Problem 21 | (A.A. Borisov)
Describe commutative semigroups whose semigroups of endomorphisms (with pointwise multiplication) are isomorphic to one of the following semigroups:
- the additive semigroup of all positive rational numbers;
- the additive semigroup of all non negative rational numbers. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 21
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,022 | AMR-113-0022 | The Lyapin's Notebook — Problem 23 | (A.A. Borisov)
Is it true that the chain rank of any finitely generated (or finitely presented) semigroup without idempotents is finite?\\
It is proved in [Borisov4] that finitely generated commutative semigroups without idempotents have finite chain rank. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 23
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,023 | AMR-113-0023 | The Lyapin's Notebook — Problem 24 | (A.A. Borisov)
Describe commutative semigroups that have exactly four endomorphisms. \\
It is proved in [Borisov3] that every finite commutative semigroup with more than four elements has at least five endomorphisms. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 24
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,024 | AMR-113-0024 | The Lyapin's Notebook — Problem 25 | In his book *Semigroups*, E.S. Lyapin emphasized that establishing connections between the properties of endomorphism semigroups and the properties of the underlying structured sets is one of the most important directions in semigroup theory. This direction may be viewed as a natural generalization of the ideas of Galo... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 25
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,025 | AMR-113-0025 | The Lyapin's Notebook — Problem 26 | (G. Mashevitzky)
Describe the endomorphism semigroup and the tower of endomorphisms (automorphisms)
- for endomorphism semigroups of semigroups free in basic classes of semigroups, in particular in the classes of idempotent, commutative Clifford, and Clifford semigroups;
- for endomorphism semigroups of algebras free... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 26
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,026 | AMR-113-0026 | The Lyapin's Notebook — Problem 27 | (G. Mashevitzky)
- Describe transformation semigroups that are closed in the pointwise topology.
- Describe endomorphism semigroups that are closed in a topology of Zarisky type.
Motivation and definitions can be found in [Cameron], [Mash1], [MPP], [Mash2]. Transformation semigroups closed in the pointwise topology ... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 27
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,027 | AMR-113-0027 | The Lyapin's Notebook — Problem 28 | (S.I. Kublanovsky)
Let $C_0$ be a class of finite $0$-simple semigroups.
Is the class $ \mathbb{K}(C_0)$ decidable, where $\mathbb{K}$ is one of the operators $\mathbb{H}\mathbb{P}, \mathbb{H} \mathbb{P}\mathbb{S}, \mathbb{S}\mathbb{H}\mathbb{P}\mathbb{S}$?\\
For all other Birkhoff operators, the answer has been obtain... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 28
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,028 | AMR-113-0028 | The Lyapin's Notebook — Problem 29 | (S.I. Kublanovsky)
- Is the class of finite $0$-simple semigroups over groups, belonging to a pseudovariety of groups with
decidable universal theory, completely solvable?
- The same question for the class of finite Brandt semigroups, under a similar restriction on maximal
subgroups. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 29
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,029 | AMR-113-0029 | The Lyapin's Notebook — Problem 30 | (S.I. Kublanovsky)
Is the class of finite regular aperiodic semigroups completely solvable?
Recall that a semigroup is aperiodic if all its subgroups are trivial. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 30
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,030 | AMR-113-0030 | The Lyapin's Notebook — Problem 31 | (S.I. Kublanovsky)
- Is the class of finite regular orthodox semigroups completely solvable?
- The same question for the class of finite regular semigroups, whose idempotents belong to a given variety of idempotent semigroups. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 31
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,031 | AMR-113-0031 | The Lyapin's Notebook — Problem 33 | (S.I. Kublanovsky)
Let $\mathbb{K}$ be one of the operators $\mathbb{H}\mathbb{P}, \mathbb{H}\mathbb{P}\mathbb{S}, \mathbb{S}\mathbb{H}\mathbb{P}, \mathbb{S}\mathbb{H}\mathbb{P}\mathbb{S}$, and let $\Phi$ be an arbitrary finite class of finite semigroups. Is the class $Cor(\mathbb{K}(\Phi))$ decidable?
For all other B... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 33
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,032 | AMR-113-0032 | The Lyapin's Notebook — Problem 34 | (E. M. Mogiljanskaja)
Does the isomorphism of power semigroups implies the isomorphism of the original semigroups in the class of finite semigroups? | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 34
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,033 | AMR-113-0033 | The Lyapin's Notebook — Problem 35 | (S.G. Bershadsky, S.I. Kublanovsky)
Find necessary and sufficient conditions for the embeddability of a regular semigroup into the power one over a periodic group.
For completely regular semigroups such conditions are inversion and periodicity (see [Bersh+Kubl]). | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 35
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,034 | AMR-113-0034 | The Lyapin's Notebook — Problem 36 | (S.G. Bershadsky, S.I. Kublanovsky)
Is every periodic commutative semigroup embeddable into the power semigroup over a periodic Abelian group?
This is true for all regular commutative semigroups and for some finite non-regular commutative semigroups (see [Bersh+Kubl]). | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 36
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,035 | AMR-113-0035 | The Lyapin's Notebook — Problem 37 | (S.G. Bershadsky, S.I. Kublanovsky)
Is it true that if every finitely generated subsemigroup of a semigroup $S$ is embeddable into the power semigroup over some periodic group then $S$ is also embeddable into the power semigroup over a periodic group? | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 37
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,036 | AMR-113-0036 | The Lyapin's Notebook — Problem 38 | (S.G. Bershadsky, S.I. Kublanovsky)
Find general embeddability criteria (necessary and/or sufficient conditions) for a semigroup to be embeddable into the power semigroup over a periodic group.
Some partial conditions were obtained in [Donald], [Bersh+Kubl] | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 38
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,037 | AMR-113-0037 | The Lyapin's Notebook — Problem 39 | (G. Mashevitzky)
Find a theorem for inclusive varieties analogous to the Birkhoff theorem for varieties; that is, determine a (minimal) set of Birkhoff type operators such that a class of semigroups forms an inclusive variety if and only if it is closed under these operators.
Inclusive varieties are known to be closed... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 39
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,038 | AMR-113-0038 | The Lyapin's Notebook — Problem 40 | (G. Mashevitzky)
Determine all inclusive varieties with finite or countable lattices of inclusive subvarieties.
A partial solution can be found in [M2]. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 40
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,039 | AMR-113-0039 | The Lyapin's Notebook — Problem 41 | (G. Mashevitzky)
- Find minimal (maximal) inclusive varieties of semigroups that cannot be defined by elementary identical inclusions.
- Describe elementary inclusive varieties of semigroups all of whose inclusive subvarieties are elementary.
- Describe nonelementary inclusive varieties of periodic semigroups whose ... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 41
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
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"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,040 | AMR-113-0040 | The Lyapin's Notebook — Problem 42 | We call two semigroups inclusively equivalent if they satisfy the same identical inclusions; equivalently if they generate the same inclusive variety.
(G. Mashevitzky)
Classify semigroups from the basic classes of semigroups up to inclusive equivalence. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 42
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,041 | AMR-113-0041 | The Lyapin's Notebook — Problem 43 | (G. Mashevitzky)
Find semigroups from the basic classes of semigroups determined by their identical inclusions up to isomorphism.
Two-element semilattice ([L1]), quasicyclic groups ([BM]) and any finite group ([M2]) are determined by identical inclusions up to isomorphism. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 43
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,042 | AMR-113-0042 | The Lyapin's Notebook — Problem 44 | (G. Mashevitzky)
Describe ordinary semigroup varieties such that their finitely generated free semigroups can be separated from each other by identical inclusions.
The variety of semilattices satisfies this condition ([M1, M01]). | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 44
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,043 | AMR-113-0043 | The Lyapin's Notebook — Problem 45 | (G. Mashevitzky)
Does there exist a nonelementary inclusive variety of idempotent semigroups? | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 45
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,044 | AMR-113-0044 | The Lyapin's Notebook — Problem 46 | (G. Mashevitzky)
Does there exist a variety of semigroups such that the class of its finite (or finitely generated) semigroups forms an elementary inclusive variety? | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 46
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,045 | AMR-113-0045 | The Lyapin's Notebook — Problem 47 | (G. Mashevitzky)
Does there exist a finite semigroup that generates an inclusive variety with an infinite lattice of inclusive subvarieties?
The lattice of inclusive subvarieties of an inclusive variety, generated by a finite group or a finite nilsemigroup is finite (see [M3]). | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 47
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,046 | AMR-113-0046 | The Lyapin's Notebook — Problem 48 | (G. Mashevitzky)
Find an algorithm that decides whether the inclusive variety generated by a given finite set of finite semigroups, can be defined by a finite system of (elementary) identical inclusions or prove that such an algorithm does not exist.
(This problem is similar to Tarski's problem for identities).
In [M4... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 48
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,047 | AMR-113-0047 | The Lyapin's Notebook — Problem 49 | (G. Mashevitzky)
- Describe classes of semigroups in which elementary inclusive varieties form a sublattice of the lattice of inclusive varieties.
- Describe nonelementary inclusive varieties that form an upper subsemilattice in the lattice of inclusive varieties within the class of periodic semigroups.
Elementary i... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 49
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,048 | AMR-113-0048 | The Lyapin's Notebook — Problem 50 | (E.S. Lyapin)
- Characterize pargoids of projections (idempotents in the semigroup of all transformations).
- Characterize the pargoids of matrix units.
- Characterize the pargoids of idempotents of the basic classes of semigroups.
Some classes of pargoids were characterized in the paper [ESL5]. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 50
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,049 | AMR-113-0049 | The Lyapin's Notebook — Problem 51 | (E.S. Lyapin)
- For the main classes of mathematical structures and natural pargoids of transformations, determine the classes of structures that are defined by these pargoids up to isomorphism.
- Find pargoids of transformations that are determined up to isomorphism by their semigroup of endomorphisms (or group of a... | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 51
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,050 | AMR-113-0050 | The Lyapin's Notebook — Problem 52 | (E.S. Lyapin)
Characterize pargoids of transformations that admit an internal semigroup extension.
Some sufficient conditions are given in [ESL6]. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 52
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,051 | AMR-113-0051 | The Lyapin's Notebook — Problem 53 | (O.M. Gornostaev, S.I. Kublanovsky)
Describe varieties of involuted semigroups for which the quasivarieties of models representable in these varieties are finitely axiomatizable.
For classical varieties such a description has been obtained in [Gorn1]. | Source list: Bershadsky, Kublanovsky, Mashevitzky - The Lyapin's Notebook: Unsolved Problems in Semigroup Theory (2026)
Source item: Problem 53
Source URL: https://arxiv.org/abs/2604.04763
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bershadsky, Kublanovsky, Mashevitzky | 2,026 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,052 | AMR-114-0001 | Hirzebruch's 1954 Problem List — Problem 1 | At the beginning of June,1953, Hirzebruch proved what he then called the ``index theorem'':
$$
\tau (M) = \langle L(p_1,\ldots,p_k),[M]\rangle \ ,
$$
where $M$ is any closed smooth oriented manifold, $\tau (M)$ is its index or signature, and $L(p_1,\ldots,p_k)$ is the $L$-polynomial
in the Pontrygain classes of $M$. La... | Source list: Kotschick - Updates on Hirzebruch's 1954 Problem List (2013)
Source item: Problem 1
Source URL: https://arxiv.org/abs/1305.4623
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Kotschick | 2,013 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,053 | AMR-114-0002 | Hirzebruch's 1954 Problem List — Problem 2 | A Pfaffian equation in $M^{2k+1}$ can be locally reduced to the normal form
$$
dx_{2k+1}+x_1dx_{k+1}+\ldots+x_rdx_{k+r}=0\ , \ \ \ \ 0\leq r\leq k\ ,
$$
where $r$ is the only local invariant, $2r+1$ being what is usually called the class of the local Pfaffian equation. The number $r$
being fixed, give a criterion to de... | Source list: Kotschick - Updates on Hirzebruch's 1954 Problem List (2013)
Source item: Problem 2
Source URL: https://arxiv.org/abs/1305.4623
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Kotschick | 2,013 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,054 | AMR-114-0003 | Hirzebruch's 1954 Problem List — Problem 3 | Let $n+d(n)$ be the minimum dimension of an Euclidean space in which the $n$-dimensional real projective space $\mathbb{P}^n$
can be differentiably imbedded. H. Hopf proved that (even for topological imbedding) $d(n)>1$; Chern proved that $d(n)>2$
if $n\neq 2^k-1$ ($k\geq 2$) and $n\neq 2^k-2$ ($k\geq 2$). Can these bo... | Source list: Kotschick - Updates on Hirzebruch's 1954 Problem List (2013)
Source item: Problem 3
Source URL: https://arxiv.org/abs/1305.4623
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Kotschick | 2,013 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,055 | AMR-114-0004 | Hirzebruch's 1954 Problem List — Problem 4 | A closed surface $M$ in the $4$-dimensional Euclidean space ${\mathbb{E}}^4$ has an induced Riemannian metric and hence a Gaussian
curvature $K$. Does there exist such a surface for which $K<0$ everywhere? In particular, does there exist a surface of genus
$2$ in ${\mathbb{E}}^4$ for which $K<0$ everywhere? | Source list: Kotschick - Updates on Hirzebruch's 1954 Problem List (2013)
Source item: Problem 4
Source URL: https://arxiv.org/abs/1305.4623
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Kotschick | 2,013 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,056 | AMR-114-0005 | Hirzebruch's 1954 Problem List — Problem 5 | Let $M^n$ be an almost-complex manifold. Choose an Hermitian structure and consider the numbers $h^{p,q}$ defined as above.
Is $h^{p,q}$ independent of the choice of the Hermitian structure? If not, give some other definition of the $h^{p,q}$ of $M^n$ which
depends only on the almost-complex structure and which general... | Source list: Kotschick - Updates on Hirzebruch's 1954 Problem List (2013)
Source item: Problem 5
Source URL: https://arxiv.org/abs/1305.4623
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Kotschick | 2,013 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,057 | AMR-114-0006 | Hirzebruch's 1954 Problem List — Problem 6 | Consider the complex projective space $\mathbb{P}_n$ as a differentiable manifold with the usual differentiable structure. Determine all
complex structures of $\mathbb{P}_n$. \mathrm{(See Problem 14.)} In particular (28*), determine all complex structures of $\mathbb{P}_n$
which can carry a K\"ahler metric. | Source list: Kotschick - Updates on Hirzebruch's 1954 Problem List (2013)
Source item: Problem 6
Source URL: https://arxiv.org/abs/1305.4623
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Kotschick | 2,013 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,058 | AMR-114-0007 | Hirzebruch's 1954 Problem List — Problem 7 | This brings us to a specifically four-dimensional problem:
Determine all complex structures of $S^2\times S^2$. | Source list: Kotschick - Updates on Hirzebruch's 1954 Problem List (2013)
Source item: Problem 7
Source URL: https://arxiv.org/abs/1305.4623
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Kotschick | 2,013 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,059 | AMR-114-0008 | Hirzebruch's 1954 Problem List — Problem 8 | Are the $h^{p,q}$ and the Chern characteristic numbers of an algebraic variety $V_n$ topological invariants of $V_n$? If not,
determine all those linear combinations of the $h^{p,q}$ and the Chern characteristic numbers which are topological invariants. | Source list: Kotschick - Updates on Hirzebruch's 1954 Problem List (2013)
Source item: Problem 8
Source URL: https://arxiv.org/abs/1305.4623
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Kotschick | 2,013 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,060 | AMR-115-0001 | Foliations and Diffeomorphism Groups — Question 1 (Virtual Euler class one conjecture) | Let $M$ be a closed hyperbolic 3-manifold whose first Betti number is at least one. Let $a \in H^2(M ; \mathbb{R})$ be an (even) integral second cohomology class of dual Thurston norm one. Is there a finite cover $p \colon \tilde{M} \rightarrow M$ and a taut foliation $\mathcal{F}$ of $\tilde{M}$ such that the Euler cl... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 1
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Virtual Euler class one conjecture | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,061 | AMR-115-0002 | Foliations and Diffeomorphism Groups — Question 2 | Let $\varphi$ be a transitive pseudo-Anosov flow on a closed, oriented 3-manifold, and let $\gamma_1,\dots, \gamma_k$ be a collection of closed orbits. Let $Z\subseteq \mathbb{R}^k$ be the closure of the set of multislopes such that simultaneous Dehn surgery on the $\gamma_i$'s results in a pseudo-Anosov flow admitting... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 2
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,062 | AMR-115-0003 | Foliations and Diffeomorphism Groups — Question 3 | Establish the following properties of $Z$:
- The corners of $Z$ are rational points.
- The accumulation points of the corners are precisely the $**S**^1\times **S**^2$ surgeries. | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 3
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,063 | AMR-115-0004 | Foliations and Diffeomorphism Groups — Question 4 | Let $(\xi_-, \xi_+)$ be a pair of cooriented contact structures with opposite signs on $M$, and assume that there exists a vector field $Z$ transverse to both $\xi_-$ and $\xi_+$, and that both of $\xi_-$ and $\xi_+$ are tight. Does $M$ admit a cooriented *Reebless* $C^0$-foliation? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 4
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,064 | AMR-115-0005 | Foliations and Diffeomorphism Groups — Question 5 | Refinements of the Eliashberg--Thurston theorem by Colin and Bowden imply that any Reebless aspherical $C^0$-foliation approximates to such pairs. As a warm-up, one could investigate the following question raised by Colin and Firmo in [colin2011paires]:
Let $(\xi_-, \xi_+)$ be a tight positive contact pair as in the p... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 5
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,065 | AMR-115-0006 | Foliations and Diffeomorphism Groups — Question 6 | Let $(\xi_-, \xi_+)$ be a pair of (co)oriented contact structures with opposite signs on $M$ which are homotopic as plane fields, and assume that both of $\xi_-$ and $\xi_+$ are tight. Does $M$ admit a cooriented *Reebless* $C^0$-foliation? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 6
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,066 | AMR-115-0007 | Foliations and Diffeomorphism Groups — Question 7 | Let $(\xi_-, \xi_+)$ be a pair of (co)oriented contact structures with opposite signs on $M$, and assume that their contact invariants pair to $1$:
\begin{align}
\langle c(\xi_-), c(\xi_+) \rangle = 1.
\end{align}
Does $M$ admit a Reebless foliation? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 7
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,067 | AMR-115-0008 | Foliations and Diffeomorphism Groups — Question 8 | Let $M$ be a closed hyperbolic 3-manifold whose first Betti number is at least one. Is every even integral second cohomology class $a \in H^2(M ; \mathbb{R})$ of dual Thurston norm one realised as the Euler class of some tight contact structure on $M$? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 8
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,068 | AMR-115-0009 | Foliations and Diffeomorphism Groups — Question 9 | The group of Engel automorphisms of the local model is very rich: it is isomorphic to the group of contactomorphisms of standard tight $\mathbb{R}^3$. However, automorphisms do not globalize (we cannot ``cut them off''). In fact, it is known, due to work of R. Montgomery, that there are Engel manifolds with very small ... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 9
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
800,069 | AMR-115-0010 | Foliations and Diffeomorphism Groups — Question 10 | Yoshi Mitsumatsu has suggested a variation of this question:
Is the automorphism group of a generic Engel manifold trivial? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 10
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | 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 |
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