Evgeny Khukhro

works on

classification of finite simple groups 1 engel elements 1 engels sink 1 finite groups 1 group order bounds 1

From the 1 of 6 linked papers with an AI index.

activity

20242026

collaborators

Showing math.GRShow all

6 papers · 1 filter

math.GR2026

On finite groups containing an element whose Engel sink is small

Evgeny Khukhro, Pavel Shumyatsky

The paper proves that for a finite group containing an element whose right or left Engel sink is small, the order of the whole group is bounded by the size of that sink, using the…

math.GR2026

Local--global generation property of commutators in finite $I ¨ $ -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.GR2026

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.GR2026

Length parameters of finite groups and their Hall subgroups

Evgeny Khukhro, Pavel Shumyatsky

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

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.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…

On finite groups containing an element whose Engel sink is small

Local--global generation property of commutators in finite I¨-soluble groups

Rank type conditions on commutators in finite groups

Length parameters of finite groups and their Hall subgroups

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

Compact groups in which commutators have finite right Engel sinks

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