{
  "id": "0810.4870",
  "version": "v2",
  "published": "2008-10-27T16:51:26.000Z",
  "updated": "2008-11-03T03:29:42.000Z",
  "title": "Elementary equivalence of right-angled Coxeter groups and graph products of finite abelian groups",
  "authors": [
    "Montserrat Casals-Ruiz",
    "Ilya Kazachkov",
    "Vladimir Remeslennikov"
  ],
  "comment": "7 pages; version 2: added a reference to David Radcliffe's rigidity result and Remark 2.4",
  "doi": "10.1112/blms/bdp103",
  "categories": [
    "math.GR",
    "math.LO"
  ],
  "abstract": "We show that graph products of finite abelian groups are elementarily equivalent if and only if they are $\\exists\\forall$-equivalent if and only if they are isomorphic. In particular, two right-angled Coxeter groups are elementarily equivalent if and only if they are isomorphic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-03T03:29:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E06",
      "20F55",
      "03C07",
      "20E99"
    ],
    "keywords": [
      "finite abelian groups",
      "right-angled coxeter groups",
      "graph products",
      "elementary equivalence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.4870C"
    }
  }
}