22 citations · 189 across the 96 of their papers we have counts for
7 papers · 1 filter
On words that are concise in residually finite groups
Cristina Acciarri, Pavel Shumyatsky
A group-word w is called concise if whenever the set of w-values in a group G is finite it always follows that the verbal subgroup w(G) is finite. More generally, a word w is said…
Coprime commutators in PSL(2,q)
Marco Antonio Pellegrini, Pavel Shumyatsky
We show that every element of PSL(2,q) is a commutator of elements of coprime orders. This is proved by showing first that in PSL(2,q) any two involutions are conjugate by an eleme…
On groups admitting a word whose values are Engel
Raimundo Bastos, Pavel Shumyatsky, Antonio Tortora +1
Let m, n be positive integers, v a multilinear commutator word and w = v^m. We prove that if G is a residually finite group in which all w-values are n-Engel, then the verbal subgr…
Commutators of elements of coprime orders in finite groups
Pavel Shumyatsky
This paper is an attempt to find out which properties of a finite group G can be expressed in terms of commutators of elements of coprime orders. A criterion of solubility of G in…
Double automorphisms of graded Lie algebras
Cristina Acciarri, Pavel Shumyatsky
We introduce the concept of a double automorphism of an A-graded Lie algebra L. Roughly, this is an automorphism of L which also induces an automorphism of the group A. It is clear…
On the Exponent of a Verbal Subgroup in a Finite Group
Pavel Shumyatsky
Let w be a multilinear commutator word. We prove that if e is a positive integer and G is a finite group in which any nilpotent subgroup generated by w-values has exponent dividing…