Justin Lynd (Aberdeen) "Fusion systems and classifying spaces"
Abstract: The Martino-Priddy conjecture asserts that two finite groups have equivalent p-completed classifying spaces if and only if their associated fusion systems at the prime p are isomorphic. This was first proved by Bob Oliver in 2004 and 2006. Andrew Chermak generalized this in 2013 by showing that each saturated fusion system over a finite p-group has a unique classifying space attached to it.
The proofs of these results depend on the classification of the finite simple groups (CFSG). The focus for this talk will be on the group theoretic aspects of joint work with George Glauberman that helped us remove the dependence of these results on the CFSG. These results concern the question: given a finite group G acting on a finite abelian p-group, when can one find a p-local subgroup H (i.e., a normalizer of a nonidentity p-subgroup) having the same fixed points on the module as does G itself?
Mar 21, 2017