{
  "id": "2107.12805",
  "version": "v1",
  "published": "2021-07-27T13:25:20.000Z",
  "updated": "2021-07-27T13:25:20.000Z",
  "title": "Whitehead algorithm for automorphisms of generalized Baumslag-Solitar groups",
  "authors": [
    "Chloé Papin"
  ],
  "comment": "42 pages, 15 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "In analogy with the free factors of a free group we define special factors of Generalized Baumslag-Solitar (GBS) groups as non-cyclic subgroups which appear in splittings over infinite cyclic groups. We give an algorithm which, given a GBS group $G$ and an element $g \\in G$, decides whether there exists a special factor $H < G$ such that $g \\in H$. This algorithm is analogous to an algorithm by Whitehead for free groups. Furthermore we prove that given $g \\in G$ there exists a unique minimal special factor containing $g$ and give an algorithm which finds it.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-27T13:25:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E08",
      "20F65"
    ],
    "keywords": [
      "generalized baumslag-solitar groups",
      "whitehead algorithm",
      "free group",
      "automorphisms",
      "unique minimal special factor containing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}