22 citations · 50 across the 14 of their papers we have counts for
14 papers
Finite groups with a soluble group of coprime automorphisms whose fixed points have bounded Engel sinks
E. I. Khukhro, P. Shumyatsky
Suppose that a finite group admits a soluble group of coprime automorphisms . We prove that if, for some positive integer , every element of the centralizer has…
Fitting height of finite groups admitting a fixed-point-free automorphism satisfying an additional polynomial identity
E. I. Khukhro, W. A. Moens
Let be a non-zero polynomial with integer coefficients. An automorphism of a group is said to satisfy the elementary abelian identity if the linear transforma…
Strong conciseness of Engel words in profinite groups
E. I. Khukhro, P. Shumyatsky
A group word is said to be strongly concise in a class of profinite groups if, for any group in , either takes at least continuum values in …
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 of a group is a set such that for every all sufficiently long commutators belong to ${…
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 of a group is a set such that for every all sufficiently long commutators belong to ${\…
The average element order and the number of conjugacy classes of finite groups
E. I. Khukhro, A. Moretó, M. Zarrin
Let be the average order of the elements of , where is a finite group. We show that there is no polynomial lower bound for in terms of , where $N\triangl…
Compact groups in which all elements have countable right Engel sinks
E. I. Khukhro, P. Shumyatsky
A right Engel sink of an element of a group is a set such that for every all sufficiently long commutators belong to ${…
Compact groups all elements of which are almost right Engel
E. I. Khukhro, P. Shumyatsky
We say that an element of a group is almost right Engel if there is a finite set such that for every all sufficiently long commutators $[...[[g,x…
Nereshennye voprosy teorii grupp. Kourovskaya tetrad'. 18-e izd. (Russian)
V. D. Mazurov, E. I. Khukhro
This is a collection of open problems in Group Theory proposed by more than 300 mathematicians from all over the world. It has been published every 2-4 years in Novosibirsk since 1…
Words and pronilpotent subgroups in profinite groups
E. I. Khukhro, P. Shumyatsky
Let be a multilinear commutator word, that is, a commutator of weight in different group variables. It is proved that if is a profinite group in which all pronilpot…
Finite p-groups with a Frobenius group of automorphisms whose kernel is a cyclic p-group
E. I. Khukhro, N. Yu. Makarenko
Suppose that a finite -group admits a Frobenius group of automorphisms with kernel that is a cyclic -group and with complement . It is proved that if the fixe…
Lie algebras admitting a metacyclic Frobenius group of automorphisms
N. Yu. Makarenko, E. I. Khukhro
Suppose that a Lie algebra admits a finite Frobenius group of automorphisms with cyclic kernel and complement such that the characteristic of the ground field does…
Finite groups and Lie rings with a metacyclic Frobenius group of automorphisms
E. I. Khukhro, N. Yu. Makarenko
Suppose that a finite group admits a Frobenius group of automorphisms FH of coprime order with cyclic kernel F and complement H such that the fixed point subgroup of t…
Frobenius groups of automorphisms and their fixed points
Evgenii I. Khukhro, Natalia Yu. Makarenko, Pavel Shumyatsky
Suppose that a finite group admits a Frobenius group of automorphisms with kernel and complement such that the fixed-point subgroup of is trivial: .…