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