Fusion Systems on a Sylow $p$-subgroup of $\mathrm{G}_2(p^n)$ or $\mathrm{PSU}_4(p^n)$

TL;DR

This paper classifies all saturated fusion systems on Sylow p-subgroups of the groups G_2(p^n) and PSU_4(p^n), providing a comprehensive understanding of their fusion structures.

Contribution

It explicitly determines all saturated fusion systems supported on these Sylow p-subgroups up to isomorphism, extending the classification in this area.

Findings

Complete classification of fusion systems on Sylow p-subgroups of G_2(p^n)

Complete classification of fusion systems on Sylow p-subgroups of PSU_4(p^n)

Results applicable for all primes p and natural numbers n

Abstract

For any prime $p$ and $S$ a $p$-group isomorphic to a Sylow $p$-subgroup of $\mathrm{G}_2(p^n)$ or $\mathrm{PSU}_4(p^n)$ with $n\in\mathbb{N}$, we determine all saturated fusion systems supported on $S$ up to isomorphism.