{
  "id": "2301.07589",
  "version": "v1",
  "published": "2023-01-18T15:08:43.000Z",
  "updated": "2023-01-18T15:08:43.000Z",
  "title": "On groups whose cogrowth series is the diagonal of a rational series",
  "authors": [
    "Alex Bishop"
  ],
  "comment": "16 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We show that if a group contains $\\mathbb{Z}^n \\times F_m$ as a finite-index subgroup, then its cogrowth series is the diagonal of a rational function for every generating set. This answers a question of Pak and Soukup on the cogrowth of virtually abelian groups; and generalises a result by Elder, Rechnitzer, Janse van Rensburg, and Wong on the cogrowth series of the Baumslag-Solitar groups $\\mathrm{BS}(N,N)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-18T15:08:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "68R15",
      "05A15",
      "20K35"
    ],
    "keywords": [
      "cogrowth series",
      "rational series",
      "janse van rensburg",
      "baumslag-solitar groups",
      "finite-index subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}