R. Guralnick

activity

20242026

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13 papers · 1 filter

math.GR2026

Forcible groups and Frattini covers

Sean Eberhard, Robert M. Guralnick, Carl Schildkraut +1

We say that a finite group $G$ *forces* a finite group $H$ if every finite cover of $G$ contains a subgroup isomorphic to $H$ , and we say $H$ is *forcible* if some finite group $G$ …

math.GR2026

Rank type conditions on commutators in finite groups

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

For a subgroup $S$ of a group $G$ , let $I_{G} (S)$ denote the set of commutators $[g, s] = g^{- 1} g^{s}$ , where $g \in G$ and $s \in S$ , so that $[G, S]$ is the subgroup generated by $I_{G} (S)$ .…

math.GR2026

Derangements in finite classical groups and characteristic polynomials of random matrices

Jason Fulman, Robert Guralnick

We first obtain explicit upper bounds for the proportion of elements in a finite classical group G with a given characteristic polynomial. We use this to complete the proof that th…

math.GR2026

On a conjecture of Peter Neumann on fixed points in permutation groups

Daniele Garzoni, Robert M. Guralnick, Martin W. Liebeck

We prove a conjecture of Peter Neumann from 1966, predicting that every finite non-regular primitive permutation group of degree $n$ contains an element fixing at least one point a…

math.GR2025

Generic stabilizers in actions of simple algebraic groups

R. M. Guralnick, R. Lawther

In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in eac…

math.GR2025

Commuting probability for conjugate subgroups of a finite group

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 \pr(H,K). We address the following question. Let P b…