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 2015Show all

9 papers · 1 filter

math.GR2015★ 1 cited

Almost Engel finite and profinite groups

E. I. Khukhro, P. Shumyatsky

Let $g$ be an element of a 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 $g$ is re…

math.GR2015

Coverings of commutators in profinite groups

Cristina Acciarri, Pavel Shumyatsky

Let $w$ be a group-word. Suppose that the set of all $w$ -values in a profinite group $G$ is contained in a union of countably many subgroups. It is natural to ask in what way the s…

math.GR2015

On conciseness of words in profinite groups

Eloisa Detomi, Marta Morigi, Pavel Shumyatsky

Let w be a group word. It is conjectured that if w has only countably many values in a profinite group G, then the verbal subgroup w(G) is finite. In the present paper we confirm t…

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 varieties of groups satisfying an Engel type identity

P. Shumyatsky, A. Tortora, M. Tota

Let m, n be positive integers, v a multilinear commutator word and w = v^m. Denote by v(G) and w(G) the verbal subgroups of a group G corresponding to v and w, respectively. We pro…

math.GR2015★ 8 cited

On profinite groups with Engel-like conditions

Raimundo Bastos, Pavel Shumyatsky

Let $G$ be a profinite group in which for every element $x \in G$ there exists a natural number $q = q (x)$ such that $x^{q}$ is Engel. We show that $G$ is locally virtually nilpotent. F…