A characterization of the groups $PSL_n(q)$ and $PSU_n(q)$ by their $2$-fusion systems, $q$ odd

TL;DR

This paper characterizes the groups PSL_n(q) and PSU_n(q) using their 2-fusion systems, contributing to the classification of finite simple groups by simplifying the proof process.

Contribution

It provides a new characterization of certain finite simple groups via their 2-fusion systems, advancing Aschbacher's program for classification.

Findings

Characterization of PSL_n(q) and PSU_n(q) by 2-fusion systems

Extension of fusion system techniques to classify finite simple groups

Supports simplified proofs in the classification program

Abstract

Let $q$ be a nontrivial odd prime power, and let $n \ge 2$ be a natural number with $(n,q) \ne (2,3)$. We characterize the groups $PSL_n(q)$ and $PSU_n(q)$ by their $2$-fusion systems. This contributes to a programme of Aschbacher aiming at a simplified proof of the classification of finite simple groups.