Centralizers of normal subsystems revisited

TL;DR

This paper reexamines key concepts in saturated fusion systems, providing new definitions and constructions for centralizers of normal subsystems and their products, enhancing theoretical understanding.

Contribution

It introduces a novel approach to defining centralizers and revisits the construction of products of normal subsystems that centralize each other.

Findings

New approach to defining centralizers of normal subsystems

Revised construction of the product of two centralizing normal subsystems

Improved theoretical framework for saturated fusion systems

Abstract

In this paper we revisit two concepts which were originally introduced by Aschbacher and are crucial in the theory of saturated fusion systems: Firstly, we give a new approach to defining the centralizer of a normal subsystem. Secondly, we revisit the construction of the product of two normal subsystems which centralize each other.