{
  "id": "math/9711203",
  "version": "v1",
  "published": "1997-11-24T00:00:00.000Z",
  "updated": "1997-11-24T00:00:00.000Z",
  "title": "The automorphism tower of a free group",
  "authors": [
    "Vladimir Tolstykh"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that the automorphism group of an arbitrary non-abelian free group is complete. It generalizes the result by J.Dyer and E.Formanek (1975) stating the completeness of automorphism group of finitely generated free groups. Using the description of involutions in automorphism groups of free groups (J. Dyer, P. Scott, 1975) we obtain a group-theoretic characterization of inner automorphisms determined by primitive elements in the automorphism group of any non-abelian free group F. It follows that the subgroup Inn(F) is characteristic in Aut(F), and hence the latter one is complete.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-11-24T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphism group",
      "automorphism tower",
      "arbitrary non-abelian free group",
      "finitely generated free groups",
      "group-theoretic characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997math.....11203T"
    }
  }
}