{
  "id": "1505.02053",
  "version": "v1",
  "published": "2015-05-08T14:46:38.000Z",
  "updated": "2015-05-08T14:46:38.000Z",
  "title": "Hyperbolic diagram groups are free",
  "authors": [
    "Anthony Genevois"
  ],
  "comment": "17 pages, 9 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "In this paper, we study the so-called diagram groups. Our main result is that diagram groups are free if and only if they do not contain any subgroup isomorphic to $\\mathbb{Z}^2$. As an immediate corollary, we get that hyperbolic diagram groups are necessarily free, answering a question of Guba and Sapir.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-08T14:46:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67"
    ],
    "keywords": [
      "hyperbolic diagram groups",
      "main result",
      "subgroup isomorphic",
      "immediate corollary",
      "necessarily free"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150502053G"
    }
  }
}