{
  "id": "1608.03538",
  "version": "v1",
  "published": "2016-08-11T17:07:16.000Z",
  "updated": "2016-08-11T17:07:16.000Z",
  "title": "Normalising graphs of groups",
  "authors": [
    "Christian Krattenthaler",
    "Thomas W. Müller"
  ],
  "comment": "16 pages, AmS-LaTeX. arXiv admin note: substantial text overlap with arXiv:1404.1258",
  "categories": [
    "math.GR"
  ],
  "abstract": "We discuss a partial normalisation of a finite graph of finite groups $(\\Gamma(-), X)$ which leaves invariant the fundamental group. In conjunction with an easy graph-theoretic result, this provides a flexible and rather useful tool in the study of finitely generated virtually free groups. Applications discussed here include (i) an important inequality for the number of edges in a Stallings decomposition $\\Gamma \\cong \\pi_1(\\Gamma(-), X)$ of a finitely generated virtually free group, (ii) the proof of equivalence of a number of conditions for such a group to be `large', as well as (iii) the classification up to isomorphism of virtually free groups of (free) rank $2$. We also discuss some number-theoretic consequences of the last result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-11T17:07:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E06",
      "20E08"
    ],
    "keywords": [
      "normalising graphs",
      "finitely generated virtually free group",
      "fundamental group",
      "finite graph",
      "stallings decomposition"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}