Timothy C. Burness

activity

20172025

most citedThe depth of a finite simple group

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

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21 papers · 1 filter

math.GR2025

On the intersections of nilpotent subgroups in simple groups

Timothy C. Burness, Hong Yi Huang

Let $G$ be a finite group and let $H_{p}$ be a Sylow $p$ -subgroup of $G$ . A recent conjecture of Lisi and Sabatini asserts the existence of an element $x \in G$ such that $H_p \cap H…

math.GR2025

On the intersections of Sylow subgroups in almost simple groups

Timothy C. Burness, Hong Yi Huang

Let $G$ be a finite almost simple group and let $H$ be a Sylow $p$ -subgroup of $G$ . As a special case of a theorem of Zenkov, there exist $x, y \in G$ such that $H \cap H^x \cap H^y…

math.GR2025

On the depth of subgroups of simple groups

Timothy C. Burness

The depth of a subgroup $H$ of a finite group $G$ is a positive integer defined with respect to the inclusion of the corresponding complex group algebras $\mathbb{C}H \subseteq \ma…

math.GR2025

On fixed-point-free involutions in actions of finite exceptional groups of Lie type

Timothy C. Burness, Mikko Korhonen

Let $G$ be a nontrivial transitive permutation group on a finite set $Ω$ . By a classical theorem of Jordan, $G$ contains a derangement, which is an element with no fixed points on…

math.GR2024

On derangements in simple permutation groups

Timothy C. Burness, Marco Fusari

Let $G ⩽ Sym (Ω)$ be a finite transitive permutation group and recall that an element in $G$ is a derangement if it has no fixed points on $Ω$ . Let $Δ (G)$ be the set o…

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…