Timothy C. Burness

activity

20242026

collaborators

7 papers

math.GR2026

On the regularity of irreducible subgroups of finite classical groups

Timothy C. Burness, Lei Wang

Let $G$ be a finite group and let $I ¨ = (H_{1}, \dots, H_{t})$ be a $t$ -tuple of core-free subgroups of $G$ . We say that $I ¨ $ is regular if $G$ contains elements $g_{1}, \dots, g_{t}$ suc…

math.GR2026

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.GR2026

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 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 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 $I^c ◯$ . By a classical theorem of Jordan, $G$ contains a derangement, which is an element with no fixed points on…

math.GR2025

On derangements in simple permutation groups

Timothy C. Burness, Marco Fusari

Let $G ⩽ Sym (I^c ◯)$ be a finite transitive permutation group and recall that an element in $G$ is a derangement if it has no fixed points on $I^c ◯$ . Let $I^ (G)$ be the se…