Trees of Fusion Systems

TL;DR

This paper introduces the concept of trees of fusion systems, providing conditions for their completion to be saturated, and demonstrates how to extend fusion systems by enlarging automorphism groups of specific subgroups.

Contribution

It defines trees of fusion systems and establishes a criterion for their saturation, advancing the understanding of fusion system extensions.

Findings

Provided a sufficient condition for the saturation of trees of fusion systems.

Developed a method to enlarge fusion systems via automorphism group extensions.

Applied the theory to extend arbitrary fusion systems.

Abstract

We define a `tree of fusion systems' and give a sufficient condition for its completion to be saturated. We apply this result to enlarge an arbitrary fusion system by extending the automorphism groups of certain of its subgroups.