22 citations · 189 across the 96 of their papers we have counts for
134 papers
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…
Rank properties of commutators in finite groups
Cristina Acciarri, Robert M. Guralnick, Evgeny Khukhro +1
For a subset of a finite group , let denote the set of commutators , where and . Suppose that a finite group has a Carter subg…
Relative commuting probability and BFC-type results for finite skew braces
Susanta Mondal, Pavel Shumyatsky, Marco Trombetti +1
We develop a probabilistic approach to the structure of finite skew left braces, motivated both by classical commuting probability in finite group theory and by the role of skew le…
Involutory automorphisms of finite groups of odd order
Pavel Shumyatsky, Gabriella Cristina de Souza
For a finite group we write to denote the nilpotent residual of , that is, the intersection of all terms of the lower central series. The following theorem is…
New variations on the theme of Baer's theorem
Martina Capasso, Liliana Lancellotti, Pavel Shumyatsky
Let and denote the -th terms of the lower and upper central series of a group , respectively. A classical theorem by R. Baer states that if has fin…
Finite groups with high commuting probability for Sylow subgroups
Eloisa Detomi, Débora Senise, Pavel Shumyatsky
Given two subsets of a finite group , we write for the probability that random elements and commute. If are subgroups, we denote by $\…