R. Guralnick

collaborators

3 papers

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.GR2025

Finite groups, commuting probability, and coprime automorphisms

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

Given two subgroups $H, K$ of a finite group $G$ , the probability that a pair of random elements from $H$ and $K$ commutes is denoted by $P r (H, K)$ . Suppose that a finite group $G$ a…

math.GR2025

On the number and sizes of double cosets of Sylow subgroups of the symmetric group

Persi Diaconis, Eugenio Giannelli, Robert M. Guralnick +4

Let $P_{n}$ be a Sylow $p$ -subgroup of the symmetric group $S_{n}$ . We investigate the number and sizes of the $P_{n} ∖ S_{n} / P_{n}$ double cosets, showing that most double cosets…

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

Finite groups, commuting probability, and coprime automorphisms

On the number and sizes of double cosets of Sylow subgroups of the symmetric group

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