M. Liebeck

activity

20112026

most citedOn the length and depth of finite groups (with an appendix by D.R. Heath-Brown)

9 citations · 29 across the 28 of their papers we have counts for

collaborators

36 papers

math.CO2026

A new flag-transitive linear space

Seyed Hassan Alavi, Ashraf Daneshkhah, Martin W. Liebeck +1

We construct a new flag-transitive $2$ - $(496, 4, 1)$ design with automorphism group $PΓL_{2} (32)$ . This corrects an omission in the classification of the finite flag-transitiv…

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

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…

math.GR2024

Involutions in finite simple groups as products of conjugates

Daniele Dona, Martin W. Liebeck, Kamilla Rekvényi

Let $G$ be a finite non-abelian simple group, $C$ a non-identity conjugacy class of $G$ , and $Γ_{C}$ the Cayley graph of $G$ based on $C \cup C^{- 1}$ . Our main result shows that in a…

math.GR2024

The binary actions of simple groups of Lie type of characteristic 2

Nick Gill, Pierre Guillot, Martin W. Liebeck

Let $C$ be a conjugacy class of involutions in a group $G$ . We study the graph $Γ (C)$ whose vertices are elements of $C$ with $g, h \in C$ conn…