{
  "id": "1901.10321",
  "version": "v1",
  "published": "2019-01-29T14:50:33.000Z",
  "updated": "2019-01-29T14:50:33.000Z",
  "title": "A note on growth of hyperbolic groups",
  "authors": [
    "Motiejus Valiunas"
  ],
  "comment": "3 pages, 1 figure; comments are welcome!",
  "categories": [
    "math.GR"
  ],
  "abstract": "The following short note provides an alternative proof of a result of Coornaert: namely, that given a non-elementary word-hyperbolic group $G$ with a finite generating set $X$, there exist constants $\\lambda,D > 1$ such that \\[ D^{-1}\\lambda^n \\leq |B_{G,X}(n)| \\leq D \\lambda^n \\] for all $n \\geq 0$, where $B_{G,X}(n)$ is the ball of radius $n$ in the Cayley graph $\\Gamma(G,X)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-29T14:50:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67",
      "20F69"
    ],
    "keywords": [
      "hyperbolic groups",
      "non-elementary word-hyperbolic group",
      "short note",
      "finite generating set",
      "cayley graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}