Automorphism Groups of Finite p-Groups: Structure and Applications
| dc.creator | Helleloid, Geir T. | |
| dc.date | 2007-11-18 | |
| dc.date.accessioned | 2026-07-07T08:43:39Z | |
| dc.date.available | 2026-07-07T08:43:39Z | |
| dc.description | This thesis has three goals related to the automorphism groups of finite $p$-groups. The primary goal is to provide a complete proof of a theorem showing that, in some asymptotic sense, the automorphism group of almost every finite $p$-group is itself a $p$-group. We originally proved this theorem in a paper with Martin; the presentation of the proof here contains omitted proof details and revised exposition. We also give a survey of the extant results on automorphism groups of finite $p$-groups, focusing on the order of the automorphism groups and on known examples. Finally, we explore a connection between automorphisms of finite $p$-groups and Markov chains. Specifically, we define a family of Markov chains on an elementary abelian $p$-group and bound the convergence rate of some of those chains. | |
| dc.description | 107 pages, Ph.D. thesis | |
| dc.identifier | https://arxiv.org/abs/0711.2816 | |
| dc.identifier | http://arxiv.org/abs/0711.2816 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142392 | |
| dc.subject | Group Theory | |
| dc.subject | Probability | |
| dc.subject | 20E36 | |
| dc.title | Automorphism Groups of Finite p-Groups: Structure and Applications | |
| dc.type | text |