Simplicity of fusion systems of finite simple groups

TL;DR

This paper classifies when the $p$-fusion systems of known finite simple groups are simple, correcting past errors and introducing new tools for analyzing saturated fusion systems.

Contribution

It provides a comprehensive classification of simple $p$-fusion systems of finite simple groups and develops new methods for analyzing saturated fusion systems.

Findings

Identifies primes for which the fusion system of each simple group is simple.

Corrects previous errors in the classification of fusion systems.

Introduces new tools for studying $O^{p'}()$ in saturated fusion systems.

Abstract

We determine for which known finite simple groups $G$ and which primes $p$ the $p$-fusion system of $G$ is simple. This means first collecting together the results that were already known (and correcting two errors made in an earlier study of this question), and then handling the remaining cases. At the same time, we develop some new tools to use when determining $O^{p'}(\mathcal{F})$ for arbitrary saturated fusion systems.