H. Huang

activity

20212026

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7 papers · 1 filter

math.GR2026

Greedy bases and relational complexity of diagonal type groups

Hong Yi Huang, Colva M. Roney-Dougal

A base for a subgroup $G$ of $Sym (Ω)$ is a sequence of elements of $Ω$ with trivial pointwise stabiliser. The size of the smallest base for $G$ is denoted $b (G)$ . There is…

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.GR2024

On the generalised Saxl graphs of permutation groups

Saul D. Freedman, Hong Yi Huang, Melissa Lee +1

A base for a finite permutation group $G \leq Sym (Ω)$ is a subset of $Ω$ with trivial pointwise stabiliser in $G$ , and the base size of $G$ is the smallest size of a base f…

math.GR2024

Fixers and derangements of finite permutation groups

Hong Yi Huang, Cai Heng Li, Yi Lin Xie

Let $G ⩽ Sym (Ω)$ be a finite transitive permutation group with point stabiliser $H$ . We say that a subgroup $K$ of $G$ is a fixer if every element of $K$ has fixed p…

math.GR2022

On base sizes for primitive groups of product type

Timothy C. Burness, Hong Yi Huang

Let $G ⩽ Sym (Ω)$ be a finite permutation group and recall that the base size of $G$ is the minimal size of a subset of $Ω$ with trivial pointwise stabiliser. There is…

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(…