A fusion system over a p-group S is a category whose objects form
the set of all subgroups of S, whose morphisms are certain
injective group homomorphisms, and which satisfies axioms first
formulated by Puig that are modelled on conjugacy relations in
finite groups. The definition was originally motivated by
representation theory, but fusion systems also have applications to
local group theory and to homotopy theory. The connection with
homotopy theory arises through classifying spaces which can be
associated to fusion systems and which have many of the nice
properties of p-completed classifying spaces of finite groups.
Beginning with a detailed exposition of the foundational material,
the authors then proceed to discuss the role of fusion systems in
local finite group theory, homotopy theory and modular
representation theory. The book serves as a basic reference and as
an introduction to the field, particularly for students and other
young mathematicians.
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