E. Khukhro

activity

20132021

most citedLie algebras admitting a metacyclic Frobenius group of automorphisms

4 citations · 5 across the 4 of their papers we have counts for

collaborators

6 papers

math.GR2021

Strong conciseness of Engel words in profinite groups

E. I. Khukhro, P. Shumyatsky

A group word $w$ is said to be strongly concise in a class $C$ of profinite groups if, for any group $G$ in $C$ , either $w$ takes at least continuum values in $G$ …

math.GR2021

Profinite groups with an automorphism of prime order whose fixed points have finite Engel sinks

E. I. Khukhro, P. Shumyatsky

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

math.GR2020

On finite groups with an automorphism of prime order whose fixed points have bounded Engel sinks

E. I. Khukhro, P. Shumyatsky

A left 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.GR2020★ 1 cited

The average element order and the number of conjugacy classes of finite groups

E. I. Khukhro, A. Moretó, M. Zarrin

Let $o (G)$ be the average order of the elements of $G$ , where $G$ is a finite group. We show that there is no polynomial lower bound for $o (G)$ in terms of $o (N)$ , where $N\triangl…

math.GR2018

Compact groups all elements of which are almost right Engel

E. I. Khukhro, P. Shumyatsky

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

math.RA2013★ 4 cited

Lie algebras admitting a metacyclic Frobenius group of automorphisms

N. Yu. Makarenko, E. I. Khukhro

Suppose that a Lie algebra $L$ admits a finite Frobenius group of automorphisms $F H$ with cyclic kernel $F$ and complement $H$ such that the characteristic of the ground field does…