22 citations · 189 across the 96 of their papers we have counts for
11 papers · 1 filter
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.