On automorphism groups of p-groups
Date
2017
Authors
Maglione, Joshua, author
Wilson, James B., advisor
Hulpke, Alexander, committee member
Penttila, Tim, committee member
Ross, Kate, committee member
Journal Title
Journal ISSN
Volume Title
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.
Description
Rights Access
Subject
filters
Lie algebras
p-groups
automorphisms