{
  "id": "0905.0295",
  "version": "v1",
  "published": "2009-05-03T22:43:27.000Z",
  "updated": "2009-05-03T22:43:27.000Z",
  "title": "On the linearity of the holomorph group of a free group on two generators",
  "authors": [
    "F. R. Cohen",
    "V. Metaftsis",
    "S. Prassidis"
  ],
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let F_n denote the free group generated by n letters. The purpose of this article is to show that Hol(F_2), the holomorph of the free group on two generators, is linear. Consequently, any split group extension of F_2 by a linear group H is linear. This result gives a large linear subgroup of Aut(F_3). A second application is that the mapping class group for genus one surfaces with two punctures is linear.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-03T22:43:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F28"
    ],
    "keywords": [
      "free group",
      "holomorph group",
      "generators",
      "split group extension",
      "large linear subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.0295C"
    }
  }
}