Date: Tuesday, October 06, 2009
Title: Simple 2Fusion Systems
Abstract: The concept of a (saturated) fusion system was introduced by Lluis Puig, moti
vated by group representation theory. It was reinvented by Broto, Levi, and Oliver,
motivated by homotopy theory. A fusion system is a category FP , whose objects
are the subgroups of the ?nite pgroup P and whose morphisms are certain injective
group homomorphisms, including all those induced by conjugations by elements of
P. If P is a Sylow psubgroup of the ?nite group G, then FP (G) has as morphisms
precisely those maps induced by conjugations by elements of G, and this provides
examples of fusion systems. Any fusion system not arising in this way is said to
be exotic. There are natural notions of normal subsystems and simple systems.
For p = 2, there is a unique oneparameter family of known exotic simple fusion
systems. It seems increasingly plausible to conjecture that these are the only exotic
simple 2fusion systems. We shall describe these examples and discuss Aschbacher's
strategy for the classi?cation of all simple 2fusion systems.
296_AnnArborabstract.pdf
Speaker: Ron Solomon
Institution: Ohio State Univ
