R. Guralnick

activity

20222026

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

1 citations · 2 across the 6 of their papers we have counts for

collaborators

7 papers

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.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…

math.GR2022★ 1 cited

Criteria for solubility and nilpotency of finite groups with automorphisms

Cristina Acciarri, Robert M. Guralnick, Pavel Shumyatsky

Let $G$ be a finite group admitting a coprime automorphism $α$ . Let $J_{G} (α)$ denote the set of all commutators $[x, α]$ , where $x$ belongs to an $α$ -invariant Sylow subgroup of $G$ .…