Abstract

In the 1960s and 70s, involution centralizer problems gave rise to several new sporadic simple groups.  With the benefit of about 30 years of hindsight, one such problem considered by Solomon also gave rise to an infinite family of exotic 2-fusion systems, namely the Benson-Solomon systems. The Benson-Solomon fusion systems are closely related to 7-dimensional orthogonal groups over fields of odd order, and they currently comprise the known simple exotic systems at the prime 2. In this talk, I'll discuss the solution to the involution centralizer problem for the Benson-Solomon systems in the context of Aschbacher's program for the classification of simple 2-fusion systems of odd type.  The Benson-Solomon problem is intertwined with the solution to Walter's Theorem for fusion systems, one of the four main steps of the program.  This is joint work with E. Henke.