On Thompson's $p$-complement theorems for saturated fusion systems

TL;DR

This paper generalizes Thompson's classical results by proving that certain saturated fusion systems with special automorphisms are nilpotent, extending the understanding of their structural properties.

Contribution

It introduces a new class of automorphisms in saturated fusion systems and proves their implications for nilpotency, generalizing Thompson's theorems.

Findings

Saturated fusion systems with specific automorphisms are nilpotent.

Generalization of Thompson's p-complement theorems to fusion systems.

Automorphisms influence the nilpotency of fusion systems.

Abstract

In this short note we prove that a saturated fusion system admitting some special type of automorphism is nilpotent. This generalizes classical results by J.G. Thompson.