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

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Showing 2021Show all

7 papers · 1 filter

math.GR2021★ 12 cited

On the commuting probability of p-elements in a finite group

Timothy C. Burness, Robert M. Guralnick, Alexander Moretó +1

Let $G$ be a finite group, let $p$ be a prime and let $Pr_{p} (G)$ be the probability that two random $p$ -elements of $G$ commute. In this paper we prove that ${\rm Pr}_p(G) > (…

math.GR2021★ 1 cited

Fixed point ratios for finite primitive groups and applications

Timothy C. Burness, Robert M. Guralnick

Let $G$ be a finite primitive permutation group on a set $Ω$ and recall that the fixed point ratio of an element $x \in G$ , denoted $fpr (x)$ , is the proportion of points in $…

math.GR2021

On the soluble graph of a finite group

Timothy C. Burness, Andrea Lucchini, Daniele Nemmi

Let $G$ be a finite insoluble group with soluble radical $R (G)$ . In this paper we investigate the soluble graph of $G$ , which is a natural generalisation of the widely studied comm…

math.GR2021

Topological generation of simple algebraic groups

Timothy C. Burness, Spencer Gerhardt, Robert M. Guralnick

Let $G$ be a simple algebraic group over an algebraically closed field and let $X$ be an irreducible subvariety of $G^{r}$ with $r ⩾ 2$ . In this paper, we consider the genera…

math.GR2021

On the classification of extremely primitive affine groups

Timothy C. Burness, Melissa Lee

Let $G$ be a finite non-regular primitive permutation group on a set $Ω$ with point stabiliser $G_{α}$ . Then $G$ is said to be extremely primitive if $G_{α}$ acts primitively on each o…

math.GR2021

On the Saxl graphs of primitive groups with soluble stabilisers

Timothy C. Burness, Hong Yi Huang

Let $G$ be a transitive permutation group on a finite set $Ω$ and recall that a base for $G$ is a subset of $Ω$ with trivial pointwise stabiliser. The base size of $G$ , denoted $b(…

math.GR2021

On soluble subgroups of sporadic groups

Timothy C. Burness

Let $G$ be an almost simple sporadic group and let $H$ be a soluble subgroup of $G$ . In this paper we prove that there exists $x, y \in G$ such that $H \cap H^{x} \cap H^{y} = 1$ , which i…