Combinatorics Seminar: Invariable generation of finite simple groups and noncontractibility of coset posets

Abstract: I will discuss joint work with Bob Guralnick and Russ Woodroofe, some of which is ongoing.  Given a finite group G, the coset poset of G is the set of all cosets of all proper subgroups of G, partially ordered by inclusion.  Given any finite poset P, one can consider the simplicial complex whose faces are totally ordered subsets of P.  This is the order complex of P.  I will explain why the order complex of the coset poset cannot be contractible.  This result relies on Smith theory and on results about invariable generation of finite simple groups, which I will define and discuss.

Host: Martha Precup