Timothy C. Burness

activity

20172021

most citedThe depth of a finite simple group

1 citations · 1 across the 3 of their papers we have counts for

collaborators

16 papers

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…

math.GR2020

Permutation groups with restricted stabilizers

Timothy C. Burness, Aner Shalev

Fix a positive integer $d$ and let $Γ_{d}$ be the class of finite groups without sections isomorphic to the alternating group $A_{d}$ . The groups in $Γ_{d}$ were studied by Babai, Camero…

math.GR2020

The spread of a finite group

Timothy C. Burness, Robert M. Guralnick, Scott Harper

A group $G$ is said to be $\frac{3}{2}$ -generated if every nontrivial element belongs to a generating pair. It is easy to see that if $G$ has this property then every proper quotie…

math.GR2020

A note on extremely primitive affine groups

Timothy C. Burness, Adam R. Thomas

Let $G$ be a finite primitive permutation group on a set $Ω$ with nontrivial point stabilizer $G_{α}$ . We say that $G$ is extremely primitive if $G_{α}$ acts primitively on each of its…

math.GR2020

The classification of extremely primitive groups

Timothy C. Burness, Adam R. Thomas

Let $G$ be a finite primitive permutation group on a set $Ω$ with nontrivial point stabilizer $G_{α}$ . We say that $G$ is extremely primitive if $G_{α}$ acts primitively on each of its…

math.GR2019

On solvable factors of almost simple groups

Timothy C. Burness, Cai Heng Li

Let $G$ be a finite almost simple group with socle $G_{0}$ . A (nontrivial) factorization of $G$ is an expression of the form $G = H K$ , where the factors $H$ and $K$ are core-free subgr…