{
  "id": "0711.2816",
  "version": "v1",
  "published": "2007-11-18T20:00:37.000Z",
  "updated": "2007-11-18T20:00:37.000Z",
  "title": "Automorphism Groups of Finite p-Groups: Structure and Applications",
  "authors": [
    "Geir T. Helleloid"
  ],
  "comment": "107 pages, Ph.D. thesis",
  "categories": [
    "math.GR",
    "math.PR"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-18T20:00:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E36"
    ],
    "keywords": [
      "automorphism group",
      "finite p-groups",
      "applications",
      "markov chains",
      "complete proof"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 107,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2816H"
    }
  }
}