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Mathematics Colloquium


Date:  Tuesday, October 06, 2009

Title:  Simple 2-Fusion 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 p-group P and whose morphisms are certain injective group homomorphisms, including all those induced by conjugations by elements of P. If P is a Sylow p-subgroup 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 one-parameter family of known exotic simple fusion systems. It seems increasingly plausible to conjecture that these are the only exotic simple 2-fusion systems. We shall describe these examples and discuss Aschbacher's strategy for the classi?cation of all simple 2-fusion systems.

Speaker:  Ron Solomon
Institution:  Ohio State Univ


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