{
  "id": "1106.2331",
  "version": "v2",
  "published": "2011-06-12T19:08:09.000Z",
  "updated": "2012-04-24T18:57:05.000Z",
  "title": "Automorphisms of Partially Commutative Groups II: Combinatorial Subgroups",
  "authors": [
    "Andrew J. Duncan",
    "Vladimir N. Remeslennikov"
  ],
  "comment": "7 figures, 63 pages. Notation and definitions clarified and typos corrected. 2 new figures added. Appendix containing details of presentation and proof of a theorem added",
  "doi": "10.1142/S0218196712500749",
  "categories": [
    "math.GR"
  ],
  "abstract": "We define several \"standard\" subgroups of the automorphism group Aut(G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut(G). If C is the commutation graph of G, we show how Aut(G) decomposes in terms of the connected components of C: obtaining a particularly clear decomposition theorem in the special case where C has no isolated vertices. If C has no vertices of a type we call dominated then we give a semi-direct decompostion of Aut(G) into a subgroup of locally conjugating automorphisms by the subgroup stabilising a certain lattice of \"admissible subsets\" of the vertices of C. We then characterise those graphs for which Aut(G) is a product (not necessarily semi-direct) of two such subgroups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-24T18:57:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20E36"
    ],
    "keywords": [
      "partially commutative groups",
      "combinatorial subgroups",
      "automorphism group aut",
      "particularly clear decomposition theorem",
      "semi-direct decompostion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.2331D"
    }
  }
}