P. Shumyatsky

works on

classification of finite simple groups 1 engel elements 1 engels sink 1 finite groups 1 group order bounds 1

From the 1 of 15 linked papers with an AI index.

collaborators

15 papers

math.GR2026

On finite groups containing an element whose Engel sink is small

Evgeny Khukhro, Pavel Shumyatsky

The paper proves that for a finite group containing an element whose right or left Engel sink is small, the order of the whole group is bounded by the size of that sink, using the…

math.GR2026

New variations on the theme of Baer's theorem

Martina Capasso, Liliana Lancellotti, Pavel Shumyatsky

Let $I^_{s}^{3} (G)$ and $Z_{s} (G)$ denote the $s$ -th terms of the lower and upper central series of a group $G$ , respectively. A classical theorem by R. Baer states that if $Z_{s} (G)$ has fi…

math.GR2026

Finite groups with high commuting probability for Sylow subgroups

Eloisa Detomi, DÃ©bora Senise, Pavel Shumyatsky

Given two subsets $X, Y$ of a finite group $G$ , we write $Pr (X, Y)$ for the probability that random elements $x \in X$ and $y \in Y$ commute. If $X, Y$ are subgroups, we denote by $\…

math.GR2026

Local--global generation property of commutators in finite $I ¨ $ -soluble groups

Cristina Acciarri, Robert M. Guralnick, Evgeny Khukhro +1

For a group $A$ acting by automorphisms on a group $G$ , let $I_{G} (A)$ denote the set of commutators $[g, a] = g^{- 1} g^{a}$ , where $g \in G$ and $a \in A$ , so that $[G, A]$ is the subgroup g…

math.GR2026

Rank type conditions on commutators in finite groups

Cristina Acciarri, Robert M. Guralnick, Evgeny Khukhro +1

For a subgroup $S$ of a group $G$ , let $I_{G} (S)$ denote the set of commutators $[g, s] = g^{- 1} g^{s}$ , where $g \in G$ and $s \in S$ , so that $[G, S]$ is the subgroup generated by $I_{G} (S)$ .…

math.GR2026

Length parameters of finite groups and their Hall subgroups

Evgeny Khukhro, Pavel Shumyatsky

Let $I ¨ $ be a set of primes containing $2$ and an odd prime $p$ . It is proved that if a finite group $G$ has a Hall $I ¨ $ -subgroup $H$ , then the non- $p$ -soluble length of $G$ is bou…

On finite groups containing an element whose Engel sink is small

New variations on the theme of Baer's theorem

Finite groups with high commuting probability for Sylow subgroups

Local--global generation property of commutators in finite I¨-soluble groups

Rank type conditions on commutators in finite groups

Length parameters of finite groups and their Hall subgroups

Local--global generation property of commutators in finite $I ¨ $ -soluble groups