Timothy C. Burness

activity

20132026

most citedOn the commuting probability of p-elements in a finite group

12 citations · 48 across the 40 of their papers we have counts for

collaborators

Showing 2017Show all

8 papers · 1 filter

math.GR2017

The length and depth of algebraic groups

Timothy C. Burness, Martin W. Liebeck, Aner Shalev

Let $G$ be a connected algebraic group. An unrefinable chain of $G$ is a chain of subgroups $G = G_{0} > G_{1} > \dots > G_{t} = 1$ , where each $G_{i}$ is a maximal connected subgroup of…

math.GR2017★ 9 cited

On the Saxl graph of a permutation group

Timothy C. Burness, Michael Giudici

Let $G$ be a permutation group on a set $Ω$ . A subset of $Ω$ is a base for $G$ if its pointwise stabiliser in $G$ is trivial. In this paper we introduce and study an associated gra…

math.GR2017

Simple groups, generation and probabilistic methods

Timothy C. Burness

It is well known that every finite simple group can be generated by two elements and this leads to a wide range of problems that have been the focus of intensive research in recent…

math.GR2017

On the uniform domination number of a finite simple group

Timothy C. Burness, Scott Harper

Let $G$ be a finite simple group. By a theorem of Guralnick and Kantor, $G$ contains a conjugacy class $C$ such that for each non-identity element $x \in G$ , there exists $y \in C$ …

math.GR2017★ 1 cited

The depth of a finite simple group

Timothy C. Burness, Martin W. Liebeck, Aner Shalev

We introduce the notion of the depth of a finite group $G$ , defined as the minimal length of an unrefinable chain of subgroups from $G$ to the trivial subgroup. In this paper we in…

math.GR2017

Simple groups, fixed point ratios and applications

Timothy C. Burness

The study of fixed point ratios is a classical topic in permutation group theory, with a long history stretching back to the origins of the subject in the 19th century. Fixed point…

math.GR2017

On the involution fixity of exceptional groups of Lie type

Timothy C. Burness, Adam R. Thomas

The involution fixity $ifix (G)$ of a permutation group $G$ of degree $n$ is the maximum number of fixed points of an involution. In this paper we study the involution fixity…

math.GR2017

$A_{1}$ -type subgroups containing regular unipotent elements

Timothy C. Burness, Donna M. Testerman

Let $G$ be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic $p > 0$ and let $X = PSL_{2} (p)$ be a subgroup of $G$ conta…

The length and depth of algebraic groups

On the Saxl graph of a permutation group

Simple groups, generation and probabilistic methods

On the uniform domination number of a finite simple group

The depth of a finite simple group

Simple groups, fixed point ratios and applications

On the involution fixity of exceptional groups of Lie type

A1​-type subgroups containing regular unipotent elements

$A_{1}$ -type subgroups containing regular unipotent elements