{
  "id": "1709.06441",
  "version": "v1",
  "published": "2017-09-19T14:14:13.000Z",
  "updated": "2017-09-19T14:14:13.000Z",
  "title": "Every group is the outer automorphism group of an HNN-extension of a fixed triangle group",
  "authors": [
    "Alan D. Logan"
  ],
  "comment": "35 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Fix an equilateral triangle group $T_i=\\langle a, b; a^i, b^i, (ab)^i\\rangle$ with $i\\geq6$ arbitrary. Our main result is: for every presentation $\\mathcal{P}$ of every countable group $Q$ there exists an HNN-extension $T_{\\mathcal{P}}$ of $T_i$ such that $\\operatorname{Out}(T_{\\mathcal{P}})\\cong Q$. We construct the HNN-extensions explicitly, and examples are given. The class of groups constructed have nice categorical and residual properties. In order to prove our main result we give a method for recognising malnormal subgroups of small cancellation groups, and we introduce the concept of \"malcharacteristic\" subgroups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-19T14:14:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F28",
      "20F65",
      "20F55"
    ],
    "keywords": [
      "outer automorphism group",
      "fixed triangle group",
      "hnn-extension",
      "main result",
      "small cancellation groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}