Normalizers of sets of components in fusion systems

TL;DR

This paper introduces new methods for constructing saturated fusion subsystems, focusing on normalizers of components, inspired by prior work on normalizers of single components and extending to multiple components.

Contribution

It presents novel techniques for constructing normalizers of sets of components in fusion systems, generalizing previous constructions for single components.

Findings

Developed new methods for constructing saturated fusion subsystems.

Extended the concept of normalizers from single components to sets of components.

Provided frameworks inspired by prior work and joint research efforts.

Abstract

We describe some new ways to construct saturated fusion subsystems, including, as a special case, the normalizer of a set of components of the ambient fusion system. This was motivated in part by Aschbacher's construction of the normalizer of one component, and in part by joint work with three other authors where we had to construct the normalizer of all of the components.