22 citations · 189 across the 96 of their papers we have counts for
8 papers · 1 filter
Locally finite groups containing a -element with Chernikov centralizer
E. I. Khukhro, N. Yu. Makarenko, P. Shumyatsky
Suppose that a locally finite group has a -element with Chernikov centralizer. It is proved that if the involution in has nilpotent centralizer, then…
Finite groups and Lie rings with an automorphism of order
E. I. Khukhro, N. Yu. Makarenko, P. Shumyatsky
Suppose that a finite group admits an automorphism of order such that the fixed-point subgroup of the involution is nilpotent of clas…
Commutators and commutator subgroups in profinite groups
Cristina Acciarri, Pavel Shumyatsky
Let be a profinite group. We prove that the commutator subgroup is finite-by-procyclic if and only if the set of all commutators of is contained in a union of countabl…
On rational and concise words
Robert Guralnick, 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…
Procyclic coverings of commutators in profinite groups
Gustavo A. Fernández-Alcober, Marta Morigi, Pavel Shumyatsky
We consider profinite groups in which all commutators are contained in a union of finitely many procyclic subgroups. It is shown that if G is a profinite group in which all commuta…
On the length of finite factorized groups
E. I. Khukhro, P. Shumyatsky
The nonsoluble length of a finite group is defined as the number of nonsoluble factors in a shortest normal series each of whose factors either is soluble or is a direct…