Evgeny Khukhro

activity

20082026

most citedAutomorphism invariance and identities

8 citations · 18 across the 17 of their papers we have counts for

collaborators

19 papers

math.GR2026

Rank properties of commutators in finite groups

Cristina Acciarri, Robert M. Guralnick, Evgeny Khukhro +1

For a subset $S$ of a finite group $G$ , let $I_{G} (S)$ denote the set of commutators $[g, x] = g^{- 1} g^{x}$ , where $g \in G$ and $x \in S$ . Suppose that a finite group $G$ has a Carter subg…

math.GR2026

Length parameters of finite groups and their Hall subgroups

Evgeny Khukhro, Pavel Shumyatsky

Let $π$ be a set of primes containing $2$ and an odd prime $p$ . It is proved that if a finite group $G$ has a Hall $π$ -subgroup $H$ , then the non- $p$ -soluble length of $G$ is bound…

math.GR2026

On finite groups containing an element whose Engel sink is small

Evgeny Khukhro, Pavel Shumyatsky

For an element $g$ of a group $G$ , a right Engel sink of $g$ is a subset of $G$ containing all sufficiently long commutators $[... [[g, x], x], \dots, x]$ for all $x \in G$ . A left Eng…

math.GR2025

On a problem of B. Hartley about a small centralizer in finite and locally finite groups

Evgeny Khukhro

It is proved that if a finite group $G$ has an automorphism of order $n$ with $m$ fixed points, then $G$ has a soluble subgroup whose index and Fitting height are bounded in terms…

math.GR2025

Local--global generation property of commutators in finite $π$ -soluble groups

Cristina Acciarri, Robert M. Guralnick, Evgeny Khukhro +1

For a group $A$ acting by automorphisms on a group $G$ , let $I_{G} (A)$ denote the set of commutators $[g, a] = g^{- 1} g^{a}$ , where $g \in G$ and $a \in A$ , so that $[G, A]$ is the subgroup g…

math.GR2024

Compact groups in which commutators have finite right Engel sinks

Evgeny Khukhro, Pavel Shumyatsky

A right Engel sink of an element $g$ of a group $G$ is a subset containing all sufficiently long commutators $[... [[g, x], x], \dots, x]$ . We prove that if $G$ is a compact group in w…

math.GR2024

Rank type conditions on commutators in finite groups

Cristina Acciarri, Robert M. Guralnick, Evgeny Khukhro +1

For a subgroup $S$ of a group $G$ , let $I_{G} (S)$ denote the set of commutators $[g, s] = g^{- 1} g^{s}$ , where $g \in G$ and $s \in S$ , so that $[G, S]$ is the subgroup generated by $I_{G} (S)$ .…

math.GR2019★ 1 cited

Compact groups with countable Engel sinks

E. I. Khukhro, P. Shumyatsky

An Engel sink of an element $g$ of a group $G$ is a set $E (g)$ such that for every $x \in G$ all sufficiently long commutators $[... [[x, g], g], \dots, g]$ belong to ${\math…

math.GR2018

Profinite groups with an automorphism whose fixed points are right Engel

C. Acciarri, E. I. Khukhro, P. Shumyatsky

An element $g$ of a group $G$ is said to be right Engel if for every $x \in G$ there is a number $n = n (g, x)$ such that $[g,_{n} x] = 1$ . We prove that if a profinite group $G$ admits…

math.GR2018★ 4 cited

Right Engel-type subgroups and length parameters of finite groups

E. I. Khukhro, P. Shumyatsky, G. Traustason

Let $g$ be an element of a finite group $G$ and let $R_{n} (g)$ be the subgroup generated by all the right Engel values $[g,_{n} x]$ over $x \in G$ . In the case when $G$ is soluble…

math.GR2017★ 1 cited

Finite groups with Engel sinks of bounded rank

E. I. Khukhro, P. Shumyatsky

For an element $g$ of a group $G$ , an Engel sink is a subset $E (g)$ such that for every $x \in G$ all sufficiently long commutators $[... [[x, g], g], \dots, g]$ belong to ${…

math.GR2016

Almost Engel compact groups

E. I. Khukhro, P. Shumyatsky

We say that a group $G$ is almost Engel if for every $g \in G$ there is a finite set $E (g)$ such that for every $x \in G$ all sufficiently long commutators $[...[[x,g],g],…

math.GR2015

Engel-type subgroups and length parameters of finite groups

Evgeny Khukhro, Pavel Shumyatsky

Let $g$ be an element of a finite group $G$ . For a positive integer $n$ , let $E_{n} (g)$ be the subgroup generated by all commutators $[... [[x, g], g], \dots, g]$ over $x \in G$ , where $g$ …

math.GR2015

On finite soluble groups with almost fixed-point-free automorphisms of non-coprime order

E. I. Khukhro

It is proved that if a finite $p$ -soluble group $G$ admits an automorphism $φ$ of order $p^{n}$ having at most $m$ fixed points on every $φ$ -invariant elementary abelian $p^{'}$ -section…

math.GR2014

Locally finite groups containing a $2$ -element with Chernikov centralizer

E. I. Khukhro, N. Yu. Makarenko, P. Shumyatsky

Suppose that a locally finite group $G$ has a $2$ -element $g$ with Chernikov centralizer. It is proved that if the involution in $⟨ g ⟩$ has nilpotent centralizer, then…

math.GR2014

On the length of finite factorized groups

E. I. Khukhro, P. Shumyatsky

The nonsoluble length $λ (G)$ of a finite group $G$ is defined as the number of nonsoluble factors in a shortest normal series each of whose factors either is soluble or is a direct…

math.GR2014

On the length of finite groups and of fixed points

E. I. Khukhro, P. Shumyatsky

The generalized Fitting height of a finite group $G$ is the least number $h = h^{*} (G)$ such that $F_{h}^{*} (G) = G$ , where the $F_{i}^{*} (G)$ is the generalized Fitting series: $F^*_1(G)=F^*(G)…

math.GR2013★ 4 cited

Nonsoluble and non-p-soluble length of finite groups

E. I. Khukhro, P. Shumyatsky

Every finite group $G$ has a normal series each of whose factors either is soluble or is a direct product of nonabelian simple groups. We define the nonsoluble length $λ (G)$ as the…

math.GR2008★ 8 cited

Automorphism invariance and identities

Evgenii I. Khukhro, Anton A. Klyachko, Natalia Yu. Makarenko +1

If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras…

Rank properties of commutators in finite groups

Length parameters of finite groups and their Hall subgroups

On finite groups containing an element whose Engel sink is small

On a problem of B. Hartley about a small centralizer in finite and locally finite groups

Local--global generation property of commutators in finite π-soluble groups

Compact groups in which commutators have finite right Engel sinks

Rank type conditions on commutators in finite groups

Compact groups with countable Engel sinks

Profinite groups with an automorphism whose fixed points are right Engel

Right Engel-type subgroups and length parameters of finite groups

Finite groups with Engel sinks of bounded rank

Almost Engel compact groups

Engel-type subgroups and length parameters of finite groups

On finite soluble groups with almost fixed-point-free automorphisms of non-coprime order

Locally finite groups containing a 2-element with Chernikov centralizer

On the length of finite factorized groups

On the length of finite groups and of fixed points

Nonsoluble and non-p-soluble length of finite groups

Automorphism invariance and identities

Local--global generation property of commutators in finite $π$ -soluble groups

Locally finite groups containing a $2$ -element with Chernikov centralizer