{
  "id": "1107.3719",
  "version": "v5",
  "published": "2011-07-19T14:09:49.000Z",
  "updated": "2014-08-27T20:07:53.000Z",
  "title": "Verbal subgroups of hyperbolic groups have infinite width",
  "authors": [
    "Alexei Myasnikov",
    "Andrey Nikolaev"
  ],
  "comment": "To appear in Journal of the London Mathematical Society. 22 pages, 8 figures",
  "doi": "10.1112/jlms/jdu034",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a non-elementary hyperbolic group. Let $w$ be a group word such that the set $w[G]$ of all its values in $G$ does not coincide with $G$ or 1. We show that the width of verbal subgroup $w(G)=<w[G]>$ is infinite. That is, there is no such $l\\in\\mathbb Z$ that any $g\\in w(G)$ can be represented as a product of $\\le l$ values of $w$ and their inverses.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-05-15T21:12:04.000Z",
      "title": "Hyperbolic groups have infinite verbal width",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2014-08-27T20:07:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67",
      "20F65"
    ],
    "keywords": [
      "verbal subgroup",
      "infinite width",
      "non-elementary hyperbolic group",
      "group word"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.3719M"
    }
  }
}