{
  "id": "2501.08747",
  "version": "v1",
  "published": "2025-01-15T12:05:47.000Z",
  "updated": "2025-01-15T12:05:47.000Z",
  "title": "Every group is the automorphism group of a graph with arbitrarily large genus",
  "authors": [
    "Marco Barbieri"
  ],
  "comment": "3 pages, comments are welcome!",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We prove that, to every abstract group $G$, we can associate a sequence of graphs $\\Gamma_n$ such that the automorphism group of $\\Gamma_n$ is isomorphic to $G$ and the genus of $\\Gamma_n$ is an unbounded function of $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-15T12:05:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C25"
    ],
    "keywords": [
      "arbitrarily large genus",
      "automorphism group",
      "abstract group",
      "isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}