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

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130 papers · 1 filter

math.GR2026

Coprime automorphisms of profinite groups and the commuting probability of Sylow subgroups

Eloisa Detomi, Robert M. Guralnick, Marta Morigi +1

Given two (closed) subgroups H, K of a profinite group G, we write Pr(H,K) for the probability that a random pair from HxK commutes. Here we are concerned with profinite groups con…

math.GR2026

Rank properties of commutators in finite groups

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

For a subset $S$ of a finite group $G$ , let $I_{G} (S)$ denote the set of commutators $[g, x] = g^{- 1} g^{x}$ , where $g \in G$ and $x \in S$ . Suppose that a finite group $G$ has a Carter subg…

math.GR2026

Involutory automorphisms of finite groups of odd order

Pavel Shumyatsky, Gabriella Cristina de Souza

For a finite group $G$ we write $γ_{\infty} (G)$ to denote the nilpotent residual of $G$ , that is, the intersection of all terms of the lower central series. The following theorem is…

math.GR2026

New variations on the theme of Baer's theorem

Martina Capasso, Liliana Lancellotti, Pavel Shumyatsky

Let $γ_{s} (G)$ 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 fin…

math.GR2026

Finite groups with high commuting probability for Sylow subgroups

Eloisa Detomi, Débora 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

Length parameters of finite groups and their Hall subgroups

Evgeny Khukhro, Pavel Shumyatsky

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