P. Shumyatsky

activity

20102026

most citedFrobenius groups of automorphisms and their fixed points

22 citations · 189 across the 96 of their papers we have counts for

collaborators

Showing 2019Show all

10 papers · 1 filter

math.GR2019

Profinite groups in which centralizers are virtually procyclic

Pavel Shumyatsky, Pavel Zalesskii

The article deals with profinite groups in which centralizers are virtually procyclic. Suppose that G is a profinite group such that the centralizer of every nontrivial element is…

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.GR2019

Exponent of a finite group admitting a coprime automorphism

Sara Rodrigues, Pavel Shumyatsky

Let $G$ be a finite group admitting a coprime automorphism $ϕ$ of order $n$ . Denote by $G_{ϕ}$ the centralizer of $ϕ$ in $G$ and by $G_{- ϕ}$ the set ${x^{- 1} x^{ϕ}; x \in G}$ . We pr…

math.GR2019

On finite-by-nilpotent groups

Eloisa Detomi, Guram Donadze, Marta Morigi +1

Let $γ_{n} = [x_{1}, \dots, x_{n}]$ be the $n$ th lower central word. Denote by $X_{n}$ the set of $γ_{n}$ -values in a group $G$ and suppose that there is a number $m$ such that $∣ g^{X_{n}} ∣ \leq m$ …

math.GR2019★ 11 cited

Strong conciseness in profinite groups

Eloisa Detomi, Benjamin Klopsch, Pavel Shumyatsky

A group word $w$ is said to be strongly concise in a class $C$ of profinite groups if, for every group $G$ in $C$ such that $w$ takes less than $2^{ℵ_{0}}$ v…

math.GR2019

Words of Engel type are concise in residually finite groups. Part II

Eloisa Detomi, Marta Morigi, Pavel Shumyatsky

Given a group-word w and a group G, the verbal subgroup w(G) is the one generated by all w-values in G. The word w is called concise if w(G) is finite whenever the set of w-values…