{
  "id": "math/0401349",
  "version": "v2",
  "published": "2004-01-26T12:52:45.000Z",
  "updated": "2004-02-04T14:28:04.000Z",
  "title": "Twisted conjugacy in free groups and Makanin's question",
  "authors": [
    "Valerij Bardakov",
    "Leonid Bokut",
    "Andrei Vesnin"
  ],
  "comment": "19 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We discuss the following question of G. Makanin from ``Kourovka notebook'': does there exist an algorithm to determine is for an arbitrary pair of words $U$ and $V$ of a free group $F_n$ and an arbitrary automorphism $\\phi \\in Aut(F_n)$ the equation $\\phi (X) U = V X$ solvable in $F_n$? We give the affirmative answer in the case when an automorphism is virtually inner, i.e. some its non-zero power is an inner automorphism of $F_n$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-02-04T14:28:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F10"
    ],
    "keywords": [
      "free group",
      "makanins question",
      "twisted conjugacy",
      "inner automorphism",
      "arbitrary automorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1349B"
    }
  }
}