Speaker: SIMON THOMAS (Rutgers University-New Brunswick)

Title: The Automorphism Tower Problem

Abstract: If G is a centerless group, then there is a natural embedding of G into its automorphism group Aut(G) obtained by sending every element to the corresponding inner automorphism. It turns out that Aut(G) is also a centerless group and hence we can inductively define the automorphism tower by: G, Aut(G), Aut(Aut(G)),..., etc. In this talk, I will discuss the question of whether the automorphism tower of every centerless group G eventually (perhaps transfinitely) reaches a fixed point; i.e. a group T such that every automorphism of T is inner.