February 8

Geir Helleloid ( UT Austin )

Automorphism Groups of Finite p-Groups

Abstract: It is reasonably difficult to find examples of finite p-groups whose automorphism group is also a p-group. Yet I'll present a theorem which, in some asymptotic sense, shows that the automorphism group of a finite p-group is almost always a p-group. The proof relies on a variety of combinatorial topics: counting subgroups of a p-group; analyzing the lower p-series of a free group via its connection to the free Lie algebra; and counting submodules of a module using Hall polynomials. This is joint work with Ursula Martin.