{
  "id": "1807.00547",
  "version": "v1",
  "published": "2018-07-02T09:09:22.000Z",
  "updated": "2018-07-02T09:09:22.000Z",
  "title": "Realisation of groups as automorphism groups in categories",
  "authors": [
    "Gareth A. Jones"
  ],
  "comment": "19 pages, 5 figures",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "It is shown that in various categories, including certain categories consisting of maps or hypermaps, oriented or unoriented, and their coverings, every countable group $A$ is isomorphic to the automorphism group of some object, which can be chosen to be finite if $A$ is finite. In particular, every finite group is isomorphic to the automorphism group of a dessin d'enfant of any given hyperbolic type. The method of proof, involving maximal subgroups of various triangle groups, yields a simple construction of a regular map whose automorphism group contains an isomorphic copy of every finite group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-02T09:09:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "14H57",
      "20B25",
      "20B27",
      "52B15",
      "57M10"
    ],
    "keywords": [
      "categories",
      "realisation",
      "finite group",
      "automorphism group contains",
      "simple construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}