R. Guralnick

most citedOn the number and sizes of double cosets of Sylow subgroups of the symmetric group

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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

Local--global generation property of commutators in finite $π$ -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★ 1 cited

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…

math.GR2024

Characters, Hall subgroups, and Normal Complements

Robert Guralnick, Gabriel Navarro

If $H$ is a Hall subgroup of a finite group $G$ , it was proven in 1989 using the classification of finite simple groups that all the irreducible complex characters of $H$ extend to…

Finite groups, commuting probability, and coprime automorphisms

Local--global generation property of commutators in finite π-soluble groups

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

Characters, Hall subgroups, and Normal Complements

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