{
  "id": "math/0602327",
  "version": "v1",
  "published": "2006-02-15T11:31:18.000Z",
  "updated": "2006-02-15T11:31:18.000Z",
  "title": "The automorphism group of a free-by-cyclic groups in rank 2",
  "authors": [
    "O. Bogopolski",
    "A. Martino",
    "E. Ventura"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $\\phi$ be an automorphism of a free group $F_n$ of rank $n$, and let $M_{\\phi}=F_n \\rtimes_{\\phi} \\mathbb{Z}$ be the corresponding mapping torus of $\\phi$. We study the group $Out(M_{\\phi})$ under certain technical conditions on $\\phi$. Moreover, in the case of rank 2, we classify the cases when this group is finite or virtually cyclic, depending on the conjugacy class of the image of $\\phi$ in $GL_2(\\mathbb{Z})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-15T11:31:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E06",
      "20E36"
    ],
    "keywords": [
      "free-by-cyclic groups",
      "automorphism group",
      "free group",
      "conjugacy class",
      "technical conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2327B"
    }
  }
}