Extensions of 𝑝-local finite groups

Abstract

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