Extensions of p-local finite groups

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