Saveliy V. Skresanov

activity

20182026

most citedThe proper definition and Wielandt-Hartley's theorem for submaximal

X

-subgroups

7 citations · 8 across the 16 of their papers we have counts for

collaborators

18 papers

math.GR2026

Polynomial-time isomorphism test for $k$ -generated extensions of abelian groups

Saveliy V. Skresanov

The group isomorphism problem asks whether two finite groups given by their Cayley tables are isomorphic or not. Although there are polynomial-time algorithms for some specific gro…

math.GR2025

On finite groups with exactly one noncommutator

Saveliy V. Skresanov

An element $x$ of a group $G$ is a commutator if it can be expressed in the form $x = a^{- 1} b^{- 1} ab$ for some $a, b \in G$ . In 2010 MacHale posed the following problem in the Kour…

math.GR2025

Rota-Baxter operators on compact simple Lie groups and algebras

Saveliy V. Skresanov

A Rota-Baxter operator on a Lie group $G$ is a smooth map $B : G \to G$ such that $B (g) B (h) = B (g B (g) h B (g)^{- 1})$ for all $g, h \in G$ . This concept was introduced in 2021…

cs.CC2025

Reduction of the group isomorphism problem to the group automorphism problem

Saveliy V. Skresanov

It is well known that the graph isomorphism problem is polynomial-time reducible to the graph automorphism problem (in fact these two problems are polynomial-time equivalent). We s…

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

Expanders and growth of normal subsets in finite simple groups of Lie type

Saveliy V. Skresanov

We show that some classical results on expander graphs imply growth results on normal subsets in finite simple groups. As one application, it is shown that given a nontrivial norma…

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.CO2023

On the automorphism group of a distance-regular graph

László Pyber, Saveliy V. Skresanov

The motion of a graph is the minimal degree of its full automorphism group. Babai conjectured that the motion of a primitive distance-regular graph on $n$ vertices of diameter grea…

math.GR2023

On the orders of composition factors in completely reducible groups

Attila Maróti, Saveliy V. Skresanov

We obtain an asymptotic upper bound for the product of the $p$ -parts of the orders of certain composition factors of a finite group acting completely reducibly and faithfully on a…

math.GR2023

On a polynomial bound for the orbital diameter of primitive affine groups

Saveliy V. Skresanov

Let $V G$ be a finite primitive affine permutation group, where $V$ is a vector space of dimension $d$ over the prime field $F_{p}$ and $G$ is an irreducible linear…

math.GR2022

Bounds for the diameters of orbital graphs of affine groups

Attila Maróti, Saveliy V. Skresanov

General bounds are presented for the diameters of orbital graphs of finite affine primitive permutation groups. For example, it is proved that the orbital diameter of a finite affi…

math.GR2022

Two-closure of rank 3 groups in polynomial time

Saveliy V. Skresanov

A finite permutation group $G$ on $Ω$ is called a rank 3 group if it has precisely three orbits in its induced action on $Ω \times Ω$ . The largest permutation group on $Ω$ having th…

cs.CC2021

The probabilistic Weisfeiler-Leman algorithm

Saveliy V. Skresanov

A probabilistic version of the Weisfeiler-Leman algorithm for computing the coherent closure of a colored graph is suggested. The algorithm is Monte Carlo and runs in time $ O(n^{1…

math.GR2020

On 2-closures of rank 3 groups

Saveliy V. Skresanov

A permutation group $G$ on $Ω$ is called a rank 3 group if it has precisely three orbits in its induced action on $Ω \times Ω$ . The largest permutation group on $Ω$ having the same…

math.GR2020★ 1 cited

On element orders in covers of $L_{4} (q)$ and $U_{4} (q)$

Mariya A. Grechkoseeva, Saveliy V. Skresanov

Suppose that $L$ is one of the finite simple groups $P S L_{4} (q)$ or $P S U_{4} (q)$ and $L$ acts on a vector space $W$ over a field whose characteristic divides $q$ . We prove that the nat…

math.GR2019★ 7 cited

The proper definition and Wielandt-Hartley's theorem for submaximal $X$ -subgroups

Danila Revin, Saveliy Skresanov, Andrey Vasil'ev

A nonempty class $X$ of finite groups is called complete if it is closed under taking subgroups, homomorphic images and extensions. We deal with a classical problem of d…

math.GR2018

Subgroups of minimal index in polynomial time

Saveliy V. Skresanov

Let $G$ be a finite group and let $H$ be a proper subgroup of $G$ of minimal index. By applying an old result of Y. Berkovich, we provide a polynomial algorithm for computing $|G :…

Polynomial-time isomorphism test for k-generated extensions of abelian groups

On finite groups with exactly one noncommutator

Rota-Baxter operators on compact simple Lie groups and algebras

Reduction of the group isomorphism problem to the group automorphism problem

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

Expanders and growth of normal subsets in finite simple groups of Lie type

Closures of permutation groups with restricted nonabelian composition factors

A generalization of the Brauer-Fowler theorem

On the automorphism group of a distance-regular graph

On the orders of composition factors in completely reducible groups

On a polynomial bound for the orbital diameter of primitive affine groups

Bounds for the diameters of orbital graphs of affine groups

Two-closure of rank 3 groups in polynomial time

The probabilistic Weisfeiler-Leman algorithm

On 2-closures of rank 3 groups

On element orders in covers of L4​(q) and U4​(q)

The proper definition and Wielandt-Hartley's theorem for submaximal X-subgroups

Subgroups of minimal index in polynomial time

Polynomial-time isomorphism test for $k$ -generated extensions of abelian groups

On element orders in covers of $L_{4} (q)$ and $U_{4} (q)$

The proper definition and Wielandt-Hartley's theorem for submaximal $X$ -subgroups