22 citations · 189 across the 96 of their papers we have counts for
11 papers · 2 filters
Nilpotent residual of fixed points
Emerson de Melo, Aline de Souza Lima, Pavel Shumyatsky
Let be a prime and a finite -group of exponent acting by automorphisms on a finite -group . Assume that has order at least . We show that if $γ_{\inf…
Words of Engel type are concise in residually finite groups
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 said to be concise if w(G) is finite whenever the set of w-val…
On profinite groups with commutators covered by countably many cosets
Eloisa Detomi, Marta Morigi, 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 cosets of subgroups. We are concerned with the question…
Orderable groups with Engel-like conditions
Pavel Shumyatsky
Let x be an element of a group G. For a positive integer n let E_n(x) be the subgroup generated by all commutators [...[[y,x],x],...,x] over y in G, where x is repeated n times. Th…
Finite groups with Engel sinks of bounded rank
E. I. Khukhro, P. Shumyatsky
For an element of a group , an Engel sink is a subset such that for every all sufficiently long commutators belong to ${…
Applications of Lie ring methods to group theory
Pavel Shumyatsky
This is an old article of 2000. Its aim is to illustrate how a Lie-theoretic result of Zelmanov enables one to treat various problems in group theory.
A criterion for metanilpotency of a finite group
Raimundo Bastos, Carmine Monetta, Pavel Shumyatsky
We prove that the th term of the lower central series of a finite group is nilpotent if and only if for any -commutators of coprime orders.
Profinite groups and the fixed points of coprime automorphisms
Cristina Acciarri, Pavel Shumyatsky
The main result of the paper is the following theorem. Let be a prime and an elementary abelian group of order . Suppose that acts coprimely on a profinite group $…
On verbal subgroups in finite and profinite groups
Cristina Acciarri, Pavel Shumyatsky
Let be a multilinear commutator word. In the present paper we describe recent results that show that if is a profinite group in which all -values are contained in a unio…
On groups with automorphisms whose fixed points are Engel
Cristina Acciarri, Pavel Shumyatsky, Danilo Sanção da Silveira
We complete the study of finite and profinite groups admitting an action by an elementary abelian group under which the centralizers of automorphisms consist of Engel elements. In…
Groups with Boundedly Finite Conjugacy Classes of Commutators
Glaucia Dierings, Pavel Shumyatsky
In 1954 B. H. Neumann discovered that if G is a group in which all conjugacy classes are finite with bounded size, then the derived group G' is finite. Later (in 1957) Wiegold foun…