The theory of $p$-local groups:  a survey
by C. Broto, R. Levi, and B. Oliver

(Universitat Autonoma de Barcelona)
(University of Aberdeen)
(Universite Paris-Nord)

This paper is a survey of recent results by the three authors, results 
which describe how the p-local fusion in a finite group  G  determines and 
is determined by the homotopy type of the p-completion of its classifying 
space  BG.  This connection then suggested to us the construction of 
certain spaces (classifying spaces of ``p-local finite groups'' and 
``p-local compact groups'') which have many of the same properties as have 
p-completed classifying spaces of finite and compact Lie groups, and which 
can be characterized in homotopy theoretic terms.  

(preprint)