On automorphism groups of p-groups

Abstract

We provide the necessary framework to use filters in computational settings, in particular for finitely generated nilpotent groups. The main motivation for this is to construct automorphisms of the group from derivations and Lie automorphisms of an associated Lie algebra. The key application of our work is a naively parallelizable algorithm to compute Aut(G), for finite p-groups G of exponent p. This algorithm comes as a consequence of several structure theorems on filters; one, which allows for parallelism, is a theorem about general decompositions of groups (e.g. central decompositions) and their automorphisms.