{
  "id": "2011.13016",
  "version": "v1",
  "published": "2020-11-25T20:53:06.000Z",
  "updated": "2020-11-25T20:53:06.000Z",
  "title": "Finite $2$-groups with exactly three automorphism orbits",
  "authors": [
    "Alexander Bors",
    "Stephen P. Glasby"
  ],
  "comment": "44 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We give a complete classification of the finite $2$-groups $G$ such that the natural action of the automorphism group $\\operatorname{Aut}(G)$ on $G$ admits exactly three orbits. By known results, this reduces the classification of all finite groups with exactly three automorphism orbits to the classification of those that are $p$-groups of exponent $p$ for some odd prime $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-25T20:53:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15",
      "20D45",
      "11A63",
      "12E20",
      "20B10"
    ],
    "keywords": [
      "automorphism orbits",
      "automorphism group",
      "finite groups",
      "natural action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}