{
  "id": "1003.1675",
  "version": "v4",
  "published": "2010-03-08T17:05:44.000Z",
  "updated": "2011-04-06T17:08:07.000Z",
  "title": "Free products of sofic groups with amalgamation over monotileably amenable groups",
  "authors": [
    "Benoit Collins",
    "Ken Dykema"
  ],
  "comment": "16 pages. Version 2 has a shorter proof of Lemma 2.2, thanks to Ion Nechita. Version 3 corrects a mistake. The previous Lemma 3.1 was incorrect. Version 3 has a new proof of the main result, but it is (apparently) weaker than in Version 2. Note that the paper's title also changed accordingly. Version 4 corrects a minor mistake around equation (4)",
  "journal": "M\\\"unster J. Math. 4 (2011), 101--118",
  "categories": [
    "math.GR",
    "math.DS",
    "math.OA"
  ],
  "abstract": "We show that free products of sofic groups with amalgamation over monotileably amenable subgroups are sofic. Consequently, so are HNN extensions of sofic groups relative to homomorphisms of monotileably amenable subgroups. We also show that families of independent uniformly distributed permutation matrices and certain families of non-random permutation matrices (essentially, those coming from quasi--actions of a sofic group) are asymptotically *-free as the matrix size grows without bound.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-04-06T17:08:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "46L54",
      "20E06"
    ],
    "keywords": [
      "sofic group",
      "free products",
      "monotileably amenable groups",
      "amalgamation",
      "monotileably amenable subgroups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.1675C"
    }
  }
}