{
  "id": "1812.01350",
  "version": "v1",
  "published": "2018-12-04T11:51:13.000Z",
  "updated": "2018-12-04T11:51:13.000Z",
  "title": "Expansive Automorphisms on Locally Compact Groups",
  "authors": [
    "Riddh Shah"
  ],
  "comment": "18 pages",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "We show that any connected locally compact group which admits an expansive automorphism is nilpotent. We also show that for any locally compact group $G$, $\\alpha\\in {\\rm Aut}(G)$ is expansive if and only if for any $\\alpha$-invariant closed subgroup $H$ which is either compact or normal, the restriction of $\\alpha$ to $H$ is expansive and the quotient map on $G/H$ corresponding to $\\alpha$ is expansive. We get a structure theorem for locally compact groups admitting expansive automorphisms. We prove that an automorphism on a non-discrete locally compact group can not be both distal and expansive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-04T11:51:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D05",
      "22D45",
      "37B05",
      "37A25",
      "22E25"
    ],
    "keywords": [
      "compact groups admitting expansive automorphisms",
      "non-discrete locally compact group",
      "invariant closed subgroup",
      "quotient map",
      "connected locally compact group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}