{
  "id": "1801.09241",
  "version": "v1",
  "published": "2018-01-28T15:25:39.000Z",
  "updated": "2018-01-28T15:25:39.000Z",
  "title": "Virtually abelian subgroups of $IA_n(Z/3)$ are abelian",
  "authors": [
    "Michael Handel",
    "Lee Mosher"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "When studying subgroups of $Out(F_n)$, one often replaces a given subgroup $H$ with one of its finite index subgroups $H_0$ so that virtual properties of $H$ become actual properties of $H_0$. In many cases, the finite index subgroup is $H_0 = H \\cap IA_n(Z/3)$. For which properties is this a good choice? Our main theorem states that being abelian is such a property. Namely, every virtually abelian subgroup of $IA_n(Z/3)$ is abelian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-28T15:25:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "57M07"
    ],
    "keywords": [
      "virtually abelian subgroup",
      "finite index subgroup",
      "main theorem states",
      "actual properties",
      "virtual properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}