An extension theory for partial groups

TL;DR

This paper develops an extension theory for partial groups, generalizing classical group extension concepts using fibre bundles of simplicial sets, with applications to fusion systems.

Contribution

It introduces a novel extension theory for partial groups grounded in fibre bundle theory, expanding the mathematical framework for fusion systems.

Findings

Extension theory for partial groups is established.

Connections between partial groups and fibre bundles are demonstrated.

Potential applications to fusion systems are discussed.

Abstract

Partial groups are a natural generalization of discrete groups recently introduced by Chermak in connection with the theory of fusion systems. In this paper we develop an extension theory for partial groups based in the classical theory of fibre bundles of simplicial sets.