{
  "id": "1408.4488",
  "version": "v1",
  "published": "2014-08-19T21:53:15.000Z",
  "updated": "2014-08-19T21:53:15.000Z",
  "title": "Infinitely presented graphical small cancellation groups are acylindrically hyperbolic",
  "authors": [
    "Dominik Gruber",
    "Alessandro Sisto"
  ],
  "comment": "34 pages, 3 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that infinitely presented graphical $C(7)$ and $Gr(7)$ small cancellation groups are acylindrically hyperbolic. In particular, infinitely presented classical $C(7)$-groups and, hence, classical $C'(\\frac{1}{6})$-groups are acylindrically hyperbolic. We also prove the analogous statements for the larger class of graphical small cancellation presentations over free products. We construct infinitely presented classical $C'(\\frac{1}{6})$-groups that provide new examples of divergence functions of groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-19T21:53:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F06",
      "20F65",
      "20F67"
    ],
    "keywords": [
      "graphical small cancellation groups",
      "acylindrically hyperbolic",
      "graphical small cancellation presentations",
      "larger class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.4488G"
    }
  }
}