Kernels of Localities

TL;DR

This paper establishes a new criterion for saturated fusion systems, explores localities with kernels, and introduces methods to construct saturated subsystems, advancing the understanding of fusion system extensions.

Contribution

It provides a sufficient condition for saturation, investigates localities with kernels, and develops new constructions for saturated subsystems in fusion systems.

Findings

Established a sufficient condition for fusion system saturation.

Analyzed localities with kernels as extensions of groups.

Developed new methods to construct saturated subsystems.

Abstract

We state a sufficient condition for a fusion system to be saturated. This is then used to investigate localities with kernels, i.e. localities which are (in a particular way) extensions of groups by localities. As an application of these results, we define and study certain products in fusion systems and localities, thus giving a new method to construct saturated subsystems of fusion systems.