{
  "id": "1706.07873",
  "version": "v1",
  "published": "2017-06-23T21:38:54.000Z",
  "updated": "2017-06-23T21:38:54.000Z",
  "title": "Outer automorphism groups of right-angled Coxeter groups are either large or virtually abelian",
  "authors": [
    "Andrew Sale",
    "Tim Susse"
  ],
  "comment": "18 pages, 2 figures. Comments welcome",
  "categories": [
    "math.GR"
  ],
  "abstract": "We generalise the notion of a separating intersection of links (SIL) to give necessary and sufficient criteria on the defining graph $\\Gamma$ of a right-angled Coxeter group $W_\\Gamma$ so that its outer automorphism group is large: that is, it contains a finite index subgroup that admits the free group $F_2$ as a quotient. When $Out(W_\\Gamma)$ is not large, we show it is virtually abelian. We also show that the same dichotomy holds for the outer automorphism groups of graph products of finite abelian groups. As a consequence, these groups have property (T) if and only if they are finite, or equivalently $\\Gamma$ contains no SIL.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-23T21:38:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "outer automorphism group",
      "right-angled coxeter group",
      "virtually abelian",
      "finite index subgroup",
      "finite abelian groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}