Sobolev Institute of Mathematics

output

19932026

most citedPhysics Interplay of the LHC and the ILC

408 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

collaborating institutions

Showing math.GRShow all

121 papers · 1 filter

math.GR2025

On generation by triality automorphisms

Danila O. Revin, Andrei V. Zavarnitsine

We clarify the structure of subgroups generated by conjugate graph automorphisms of order $3$ of $O_{8}^{+} (2)$ and $O_{8}^{+} (3)$ . As a result, we obtain a correction to a paper by S. Gue…

math.GR2025

Random unipotent Sylow subgroups of groups of Lie type of bounded rank

Saveliy V. Skresanov

In 2001 Liebeck and Pyber showed that a finite simple group of Lie type is a product of $25$ carefully chosen unipotent Sylow subgroups. Later, in a series of works it was shown…

math.GR2024

Explicit inverse Shapiro isomorphism and its application

Andrei V. Zavarnitsine

We find an explicit form of the inverse isomorphism from Shapiro's lemma in terms of inhomogeneous cocycles and apply it to construct special nonsplit coverings of groups with a un…

math.GR2024

On finite groups isospectral to groups with abelian Sylow $2$ -subgroups

M. A. Grechkoseeva, A. V. Vasil'ev

The spectrum of a finite group is the set of orders of its elements. We are concerned with finite groups having the same spectrum as a direct product of nonabelian simple groups wi…

math.GR2024★ 1 cited

Groups elementarily equivalent to metabelian Baumslag $-$ Solitar groups and regular bi-interpretability

Evelina Daniyarova, Alexei Myasnikov

We prove that metabelian Baumslag $-$ Solitar group $B S (1, k)$ , $k > 1$ , is (strongly) regularly bi-interpretable with the ring of integers $Z$ , and describe in algebraic terms…

math.GR2024

Closures of permutation groups with restricted nonabelian composition factors

Ilia Ponomarenko, Saveliy V. Skresanov, Andrey V. Vasil'ev

Given a permutation group $G$ on a finite set $Ω$ , let $G^{(k)}$ denote the $k$ -closure of $G$ , that is, the largest permutation group on $Ω$ having the same orbits in the induced…

math.GR2024

A generalization of the Brauer-Fowler theorem

Saveliy V. Skresanov

The famous Brauer-Fowler theorem states that the order of a finite simple group can be bounded in terms of the order of the centralizer of an involution. Using the classification o…

math.GR2023

On recognition of the direct squares of the simple groups with abelian Sylow 2-subgroups

Tao Li, A. R. Moghaddamfar, Andrey V. Vasil'ev +1

The spectrum of a group is the set of orders of its elements. Finite groups with the same spectra as the direct squares of the finite simple groups with abelian Sylow 2-subgroups a…

math.GR2023★ 1 cited

On computing the closures of solvable permutation groups

Ilia Ponomarenko, Andrey V. Vasil'ev

Let $m \geq 3$ be an integer. It is proved that the $m$ -closure of a given solvable permutation group of degree $n$ can be constructed in time $n^{O (m)}$ .

math.GR2023★ 4 cited

Equations over solvable groups

Anton A. Klyachko, Mikhail A. Mikheenko, Vitaly A. Roman'kov

Not any nonsingular equation over a metabelian group has solution in a larger metabelian group. However, any nonsingular equation over a solvable group with a subnormal series with…

math.GR2023

The spectra of almost simple groups with socle $E_{7} (q)$

Alexander A. Buturlakin, Maria A. Grechkoseeva

We give an explicit description of the set of element orders for every almost simple group with socle $E_{7} (q)$ .

math.GR2023★ 1 cited

On $p$ -index extremal groups

Andrey V. Vasil'ev, Ilya B. Gorshkov

The question on connection between the structure of a finite group $G$ and the properties of the indices of elements of $G$ has been a popular research topic for many years. The $p…

math.GR2022★ 1 cited

On generations by conjugate elements in almost simple groups with socle $\mbox{}^2F_4(q^2)'$

Danila O. Revin, Andrei V. Zavarnitsine

We prove that if $L=\mbox{}^2F_4(2^{2n+1})'$ and $x$ is a nonidentity automorphism of $L$ then $G = ⟨ L, x ⟩$ has four elements conjugate to $x$ that generate $G$ . This res…

math.GR2022

On recognition of direct powers of finite simple linear groups by spectrum

N. Yang, I. B. Gorshkov, A. M. Staroletov +1

The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the Kourovka Notebook proving that for every positive intege…

math.GR2022★ 1 cited

On embedding theorems for $X$ -subgroups

Wenbin Guo, Danila O. Revin, Andrey V. Vasil'ev

Let $X$ be a class of finite groups closed under subgroups, homomorphic images, and extensions. We study the question which goes back to the lectures of H. Wielandt in 1…

math.GR2022

The minimal size of a generating set for primitive $\frac{3}{2}$ -transitive groups

Dmitry Churikov, Andrey V. Vasil'ev, Maria A. Zvezdina

We refer to $d (G)$ as the minimal cardinality of a generating set of a finite group $G$ , and say that $G$ is $d$ -generated if $d (G) \leq d$ . A transitive permutation group $G$ is ca…

math.GR2022★ 3 cited

Criterion of nonsolvability of a finite group and recognition of direct squares of simple groups

Zh. Wang, A. V. Vasil'ev, M. A. Grechkoseeva +1

The spectrum $ω (G)$ of a finite group $G$ is the set of orders of its elements. The following sufficient criterion of nonsolvability is proved: if among the prime divisors of the o…

math.GR2021★ 2 cited

On Cayley representations of central Cayley graphs over almost simple groups

Jin Guo, Wenbin Guo, Grigory Ryabov +1

A Cayley graph over a group $G$ is said to be central if its connection set is a normal subset of $G$ . We prove that every central Cayley graph over a simple group $G$ has at most…

math.GR2021★ 7 cited

On the sharp Baer--Suzuki theorem for $π$ -radicals: sporadic groups

Nanying Yang, Zhenfeng Wu, Danila O. Revin

Let $π$ be a proper subset of the set of all primes. Denote by $r$ the smallest prime which does not belong to $π$ and set $m = r$ if $r = 2$ or $3$ and $m = r - 1$ if $r \geqslant 5…

math.GR2021★ 15 cited

Finite groups isospectral to simple groups

Maria A. Grechkoseeva, Victor D. Mazurov, Wujie Shi +2

The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectr…

math.GR2021

When is the search of relatively maximal subgroups reduced to quotients?

Wenbin Guo, Danila O. Revin

Let $X$ be a class of finite groups closed under taking subgroups, homomorphic images, and extensions. Denote by $k_{X} (G)$ the number of conjuga…

math.GR2021★ 4 cited

On the prime graph of a finite group with unique nonabelian composition factor

Maria A. Grechkoseeva, Andrey V. Vasil'ev

We say that finite groups are isospectral if they have the same sets of orders of elements. It is known that every nonsolvable finite group $G$ isospectral to a finite simple group…

math.GR2021★ 25 cited

Rota-Baxter operators on groups

Valeriy G. Bardakov, Vsevolod Gubarev

Theory of Rota-Baxter operators on rings and algebras has been developed since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined the notion of Rota-Baxter o…

math.GR2021★ 51 cited

Rota-Baxter groups, skew left braces, and the Yang-Baxter equation

Valeriy G. Bardakov, Vsevolod Gubarev

Braces were introduced by W. Rump in 2006 as an algebraic system related to the quantum Yang-Baxter equation. In 2017, L. Guarnieri and L. Vendramin defined for the same purposes a…

On generation by triality automorphisms

Random unipotent Sylow subgroups of groups of Lie type of bounded rank

Explicit inverse Shapiro isomorphism and its application

On finite groups isospectral to groups with abelian Sylow 2-subgroups

Groups elementarily equivalent to metabelian Baumslag−Solitar groups and regular bi-interpretability

Closures of permutation groups with restricted nonabelian composition factors

A generalization of the Brauer-Fowler theorem

On recognition of the direct squares of the simple groups with abelian Sylow 2-subgroups

On computing the closures of solvable permutation groups

Equations over solvable groups

The spectra of almost simple groups with socle E7​(q)

On p-index extremal groups

On generations by conjugate elements in almost simple groups with socle $\mbox{}^2F_4(q^2)'$

On recognition of direct powers of finite simple linear groups by spectrum

On embedding theorems for X-subgroups

The minimal size of a generating set for primitive 23​-transitive groups

Criterion of nonsolvability of a finite group and recognition of direct squares of simple groups

On Cayley representations of central Cayley graphs over almost simple groups

On the sharp Baer--Suzuki theorem for π-radicals: sporadic groups

Finite groups isospectral to simple groups

When is the search of relatively maximal subgroups reduced to quotients?

On the prime graph of a finite group with unique nonabelian composition factor

Rota-Baxter operators on groups

Rota-Baxter groups, skew left braces, and the Yang-Baxter equation

On finite groups isospectral to groups with abelian Sylow $2$ -subgroups

Groups elementarily equivalent to metabelian Baumslag $-$ Solitar groups and regular bi-interpretability

The spectra of almost simple groups with socle $E_{7} (q)$

On $p$ -index extremal groups

On embedding theorems for $X$ -subgroups

The minimal size of a generating set for primitive $\frac{3}{2}$ -transitive groups

On the sharp Baer--Suzuki theorem for $π$ -radicals: sporadic groups