M. Liebeck

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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.GR2024

Conjugacy in finite classical groups

Giovanni De Franceschi, Martin W. Liebeck, E. A. O'Brien

Let $G$ be a classical group defined over a finite field. We consider the following fundamental problems concerning conjugacy in $G$ : 1. List a representative for each conjugacy cl…

math.GR2024

Representations of extensions of simple groups

Scott Harper, Martin W. Liebeck

Feit and Tits (1978) proved that a nontrivial projective representation of minimal dimension of a finite extension of a finite nonabelian simple group $G$ factors through a project…

math.GR2024

Maps, simple groups, and arc-transitive graphs

Martin W. Liebeck, Cheryl E. Praeger

We determine all factorisations $X = A B$ , where $X$ is a finite almost simple group and $A, B$ are core-free subgroups such that $A \cap B$ is cyclic or dihedral. As a main application…