EXTENSIONS OF p-LOCAL FINITE GROUPS
C. Broto, N. Castellana, J. Grodal, R. Levi, and B. Oliver
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.