H. Huang

activity

20242026

collaborators

6 papers

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 $Sym (I^c ◯)$ is a sequence of elements of $I^c ◯$ with trivial pointwise stabiliser. The size of the smallest base for $G$ is denoted $b (G)$ . There…

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 generalised Saxl graphs of permutation groups

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

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

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

Fixers and derangements of finite permutation groups

Hong Yi Huang, Cai Heng Li, Yi Lin Xie

Let $G ⩽ Sym (I^c ◯)$ 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…

math.GR2024

On finite permutation groups of rank three

Hong Yi Huang, Cai Heng Li, Yan Zhou Zhu

The classification of the finite primitive permutation groups of rank $3$ was completed in the 1980s and this landmark achievement has found a wide range of applications. In the ge…