The Thompson-Lyons transfer lemma for fusion systems

TL;DR

This paper generalizes the Thompson-Lyons transfer lemma to saturated fusion systems and strengthens Alperin's fusion theorem within this framework, advancing the theoretical understanding of fusion systems.

Contribution

It introduces a generalized transfer lemma and a strengthened Alperin's fusion theorem for saturated fusion systems, extending prior results in group theory.

Findings

Generalization of Thompson transfer lemma to fusion systems

Strengthened version of Alperin's fusion theorem

Framework for analyzing fusion in saturated systems

Abstract

In this note, a generalization of the Thompson transfer lemma and its various extensions, most recently due to Lyons, is proven in the context of saturated fusion systems. A strengthening of Alperin's fusion theorem is also given in this setting, following Alperin's own "up and down" fusion.