Normalizers and centralizers of subnormal subsystems of fusion systems

TL;DR

This paper develops a framework for defining and analyzing normalizers and centralizers of subnormal subsystems within fusion systems using the concept of regular localities, advancing the structural understanding of fusion systems.

Contribution

It introduces a new notion of normalizers and centralizers for subnormal subsystems of fusion systems based on regular localities, extending existing theory.

Findings

Defines normalizers and centralizers for subnormal subsystems

Establishes properties of these notions within regular localities

Provides a foundation for further structural analysis of fusion systems

Abstract

Every saturated fusion system corresponds to a group-like structure called a regular locality. In this paper we study (suitably defined) normalizers and centralizers of partial subnormal subgroups of regular localities. This leads to a reasonable notion of normalizers and centralizers of subnormal subsystems of fusion systems.