Reduction Theorems for Generalised Block Fusion Systems

TL;DR

This paper extends classical reduction theorems to generalized block fusion systems and applies these results to demonstrate non-exoticity of fusion systems in certain finite groups of Lie type.

Contribution

It generalizes key theorems in fusion system theory and applies them to new classes of groups, broadening the understanding of fusion system properties.

Findings

Extended the Third Main Theorem by Brauer to generalized block fusion systems.

Generalized the Fong Reduction theorems for broader fusion system classes.

Proved non-exoticity of fusion systems of unipotent blocks in finite groups of Lie type.

Abstract

We generalise the Third Main Theorem by Brauer, the First and Second Fong Reduction to generalised block fusion systems and apply the Second Fong Reduction to extend a result by Cabanes about the non-exoticity of fusion systems of unipotent blocks for finite groups of Lie type.