22 citations · 189 across the 96 of their papers we have counts for
6 papers · 1 filter
On just-infinite periodic locally soluble groups
Rostislav Grigorchuk, Pavel Shumyatsky
We construct an uncountable family of periodic locally soluble groups which are hereditarily just infinite. We also show that the associated full C*-algebra C*(G) is just infinite…
Almost Engel linear groups
Pavel Shumyatsky
We prove that if a linear group is almost Engel, then is finite-by-hypercentral. If is almost nil, then is finite-by-nilpotent.
Almost Engel compact groups
E. I. Khukhro, P. Shumyatsky
We say that a group is almost Engel if for every there is a finite set such that for every all sufficiently long commutators $[...[[x,g],g],…
On just-infiniteness of locally finite groups and their C*-algebras
V. Belyaev, R. Grigorchuk, P. Shumyatsky
We give a construction of a family of locally finite residually finite groups with just-infinite C*-algebra. This answers a question from [2]. Additionally, we show that residually…
A Sufficient Condition for Nilpotency of the Commutator Subgroup
Raimundo Bastos, Pavel Shumyatsky
Let be a finite group with the property that if are commutators of coprime orders, then . We show that is nilpotent.
On finite groups with automorphisms whose fixed points are Engel
Pavel Shumyatsky, Danilo Sanção da Silveira
The main result of the paper is the following theorem. Let be a prime, a positive integer and an elementary abelian group of order . Suppose that acts coprimel…