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 2020Show all

8 papers · 1 filter

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

Almost elusive permutation groups

Timothy C. Burness, Emily V. Hall

Let $G$ be a nontrivial transitive permutation group on a finite set $Ω$ . An element of $G$ is said to be a derangement if it has no fixed points on $Ω$ . From the orbit counting le…

math.GR2020

Finite groups, minimal bases and the intersection number

Timothy C. Burness, Martino Garonzi, Andrea Lucchini

Let $G$ be a finite group and recall that the Frattini subgroup $Frat (G)$ is the intersection of all the maximal subgroups of $G$ . In this paper, we investigate the intersect…

math.GR2020

On the involution fixity of simple groups

Timothy C. Burness, Elisa Covato

Let $G$ be a finite permutation group of degree $n$ and let $ifix (G)$ be the involution fixity of $G$ , which is the maximum number of fixed points of an involution. In this p…

math.GR2020★ 1 cited

Base sizes for primitive groups with soluble stabilisers

Timothy C. Burness

Let $G$ be a finite primitive permutation group on a set $Ω$ with point stabiliser $H$ . Recall that a subset of $Ω$ is a base for $G$ if its pointwise stabiliser is trivial. We def…

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…