Saturated Fusion Systems on Sylow $p$-subgroups of Rank $2$ Simple Groups of Lie Type

TL;DR

This paper classifies all saturated fusion systems on Sylow p-subgroups of rank 2 simple Lie type groups, providing a comprehensive understanding of their fusion patterns in characteristic p.

Contribution

It explicitly determines all saturated fusion systems on these Sylow p-subgroups, a previously unresolved classification problem in group theory.

Findings

Complete classification of saturated fusion systems on Sylow p-subgroups

Identification of isomorphism classes of these fusion systems

Insights into fusion patterns in rank 2 simple groups of Lie type

Abstract

For any prime $p$ and $S$ a $p$-group isomorphic to a Sylow $p$-subgroup of a rank $2$ simple group of Lie type in characteristic $p$, we determine all saturated fusion systems supported on $S$ up to isomorphism.