  We define here two new classes of saturated fusion systems, reduced fusion
systems and tame fusion systems. These are motivated by our attempts to better
understand and search for exotic fusion systems: fusion systems which are not
the fusion systems of any finite group. Our main theorems say that every
saturated fusion system reduces to a reduced fusion system which is tame only
if the original one is realizable, and that every reduced fusion system which
is not tame is the reduction of some exotic (nonrealizable) fusion system.

Algebraic Topology;Group Theory