Extension of p-local finite groups

TL;DR

This paper studies and classifies extensions of p-local finite groups, providing insights into their structure and fundamental groups, which are crucial for understanding their classifying spaces and related algebraic topology properties.

Contribution

It introduces a classification framework for extensions of p-local finite groups and computes their fundamental groups, advancing the understanding of their algebraic and topological structure.

Findings

Classification of extensions of p-local finite groups

Computation of the fundamental group of their classifying spaces

Insights into the structure of p-local finite groups

Abstract

A p-local finite group consists of a finite p-group S, together with a pair of categories which encode ``conjugacy'' relations among subgroups of S, and which are modelled on the fusion in a Sylow p-subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as p-completed classifying spaces of finite groups. In this paper, we study and classify extensions of p-local finite groups, and also compute the fundamental group of the classifying space of a p-local finite group.