{
  "id": "1808.06371",
  "version": "v1",
  "published": "2018-08-20T10:06:57.000Z",
  "updated": "2018-08-20T10:06:57.000Z",
  "title": "Rational Growth in Virtually Abelian Groups",
  "authors": [
    "Alex Evetts"
  ],
  "comment": "29 pages. Comments are welcome",
  "categories": [
    "math.GR"
  ],
  "abstract": "We show that any subgroup of a finitely generated virtually abelian group $G$ grows rationally relative to $G$, that the set of right cosets of any subgroup of $G$ grows rationally, and that the set of conjugacy classes of $G$ grows rationally. These results hold regardless of the choice of finite weighted generating set for $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-20T10:06:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E45",
      "05E15"
    ],
    "keywords": [
      "rational growth",
      "finitely generated virtually abelian group",
      "right cosets",
      "conjugacy classes",
      "finite weighted generating set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}