M. Liebeck

activity

20152021

most citedSurjective word maps and Burnsides

p^{a} q^{b}

theorem

1 citations · 2 across the 7 of their papers we have counts for

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17 papers · 1 filter

math.GR2021

Cherlin's conjecture on finite primitive binary permutation groups

Nick Gill, Martin W. Liebeck, Pablo Spiga

A permutation group is {\it binary} if its orbits on $k$ -tuples, for any integer $k \geq 2$ , can be deduced from its orbits on $2$ -tuples. Cherlin conjectured that a finite primitiv…

math.GR2020

McKay graphs for alternating and classical groups

M. W. Liebeck, A. Shalev, Pham Huu Tiep

Let $G$ be a finite group, and $α$ a nontrivial character of $G$ . The McKay graph $M (G, α)$ has the irreducible characters of $G$ as vertices, with an edge from $χ_{1}$ to $…

math.GR2019

On the diameters of McKay graphs for finite simple groups

Martin W. Liebeck, Aner Shalev, Pham Huu Tiep

Let $G$ be a finite group, and $α$ a nontrivial character of $G$ . The McKay graph $M (G, α)$ has the irreducible characters of $G$ as vertices, with an edge from $χ_{1}$ to…

math.GR2019

Girth, words and diameter

Martin W. Liebeck, Aner Shalev

We study the girth of Cayley graphs of finite classical groups G on random sets of generators. Our main tool is an essentially best possible bound we obtain on the probability that…

math.GR2018

Zero-one generation laws for finite simple groups

Robert M. Guralnick, Martin W. Liebeck, Frank Lübeck +1

Let $G$ be a simple algebraic group over the algebraic closure of $GF (p)$ ( $p$ prime), and let $G (q)$ denote a corresponding finite group of Lie type over $GF (q)$ , where $q$ is a p…

math.GR2018

Character ratios, representation varieties and random generation of finite groups of Lie type

Martin W. Liebeck, Aner Shalev, Pham H. Tiep

We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie…