P. Shumyatsky

activity

20102026

most citedFrobenius groups of automorphisms and their fixed points

22 citations · 189 across the 96 of their papers we have counts for

collaborators

Showing 2018Show all

10 papers · 1 filter

math.GR2018

Fitting subgroup and nilpotent residual of fixed points

Emerson de Melo, Pavel Shumyatsky

Let $q$ be a prime and $A$ an elementary abelian group of order at least $q^{3}$ acting by automorphisms on a finite $q^{'}$ -group $G$ . It is proved that if $|γ_{\infty}(C_{G}(a))|\leq…

math.GR2018

Profinite groups with pronilpotent centralizers

Pavel Shumyatsky

The article deals with profinite groups in which the centralizers are pronilpotent (CN-groups). It is shown that such groups are virtually pronilpotent. More precisely, let G be a…

math.GR2018

Engel sinks of fixed points in finite groups

Cristina Acciarri, Pavel Shumyatsky, Danilo Sanção da Silveira

For an element $g$ of a group $G$ , an Engel sink is a subset $E (g)$ such that for every $x \in G$ all sufficiently long commutators $[x, g, g, \dots, g]$ belong to $\math…

math.GR2018

Profinite groups with an automorphism whose fixed points are right Engel

C. Acciarri, E. I. Khukhro, P. Shumyatsky

An element $g$ of a group $G$ is said to be right Engel if for every $x \in G$ there is a number $n = n (g, x)$ such that $[g,_{n} x] = 1$ . We prove that if a profinite group $G$ admits…

math.GR2018★ 4 cited

Right Engel-type subgroups and length parameters of finite groups

E. I. Khukhro, P. Shumyatsky, G. Traustason

Let $g$ be an element of a finite group $G$ and let $R_{n} (g)$ be the subgroup generated by all the right Engel values $[g,_{n} x]$ over $x \in G$ . In the case when $G$ is soluble…

math.GR2018★ 5 cited

Compact groups all elements of which are almost right Engel

E. I. Khukhro, P. Shumyatsky

We say that an element $g$ of a group $G$ is almost right Engel if there is a finite set $R (g)$ such that for every $x \in G$ all sufficiently long commutators $[...[[g,x…