{
  "id": "math/0505572",
  "version": "v3",
  "published": "2005-05-26T15:15:45.000Z",
  "updated": "2005-06-10T20:28:30.000Z",
  "title": "Amenability of Universal 2-Grigorchuk group",
  "authors": [
    "Roman Muchnik"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We consider the universal Grigorchuk 2-group, i.e., the group such that every Grigorchuk 2-group is a quotient. We show that this group has a nice universal representation in the group of all functions f:{0,1,2}^N --> Aut(T_2), where T_2 is a group of automorphism of the binary tree. Finally, we prove that this universal Grigorchuk 2-group is amenable. The proof is an application of the ``Munchhausen trick'' developed by V. Kaimanovich.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-06-10T20:28:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "amenability",
      "universal grigorchuk",
      "nice universal representation",
      "binary tree",
      "munchhausen trick"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5572M"
    }
  }
}