22 citations · 189 across the 96 of their papers we have counts for
8 papers · 1 filter
Words and pronilpotent subgroups in profinite groups
E. I. Khukhro, P. Shumyatsky
Let be a multilinear commutator word, that is, a commutator of weight in different group variables. It is proved that if is a profinite group in which all pronilpot…
On finite groups in which coprime commutators are covered by few cyclic subgroups
Cristina Acciarri, Pavel Shumyatsky
The coprime commutators and were recently introduced as a tool to study properties of finite groups that can be expressed in terms of commutators of elements of cop…
Nonsoluble and non-p-soluble length of finite groups
E. I. Khukhro, P. Shumyatsky
Every finite group has a normal series each of whose factors either is soluble or is a direct product of nonabelian simple groups. We define the nonsoluble length as the…
On countable coverings of word values in profinite groups
Eloisa Detomi, Marta Morigi, Pavel Shumyatsky
We prove the following results. Let w be a multilinear commutator word. If G is a profinite group in which all w-values are contained in a union of countably many periodic subgroup…
Commutators and pronilpotent subgroups in profinite groups
Eloisa Detomi, Marta Morigi, Pavel Shumyatsky
Let G be a profinite group in which all pronilpotent subgroups generated by commutators are periodic. We prove that G' is locally finite.
On locally graded groups with a word whose values are Engel
Pavel Shumyatsky, Antonio Tortora, Maria Tota
Let m, n be positive integers, v a multilinear commutator word and w = v^m. We prove that if G is a locally graded group in which all w-values are n-Engel, then the verbal subgroup…