{
  "id": "1009.5051",
  "version": "v3",
  "published": "2010-09-26T02:27:45.000Z",
  "updated": "2012-03-06T01:38:20.000Z",
  "title": "On groups whose geodesic growth is polynomial",
  "authors": [
    "Martin Bridson",
    "Jose Burillo",
    "Murray Elder",
    "Zoran Sunic"
  ],
  "comment": "11 pages, 1 figure",
  "doi": "10.1142/S0218196712500488",
  "categories": [
    "math.GR"
  ],
  "abstract": "This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely generated group $G$ has an element whose normal closure is abelian and of finite index, then $G$ has a finite generating set with respect to which the geodesic growth is polynomial (this includes all virtually cyclic groups).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-03-06T01:38:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "finite generating set",
      "polynomial",
      "observations concerning geodesic growth functions",
      "exponential geodesic growth",
      "nilpotent group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.5051B"
    }
  }
}