{
  "id": "1305.2408",
  "version": "v1",
  "published": "2013-05-10T19:33:19.000Z",
  "updated": "2013-05-10T19:33:19.000Z",
  "title": "Non-amenability of product replacement graphs",
  "authors": [
    "Anton Malyshev"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We prove non-amenability of the product replacement graphs \\Gamma_n(G) for uniformly non-amenable groups. We also prove it for Z-large groups, when n is sufficiently large. It follows that \\Gamma_n(G) is non-amenable when n is sufficiently large for hyperbolic groups, linear groups, and elementary amenable groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-10T19:33:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "product replacement graphs",
      "non-amenability",
      "sufficiently large",
      "z-large groups",
      "hyperbolic groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2408M"
    }
  }
}