{
  "id": "1508.04523",
  "version": "v1",
  "published": "2015-08-19T04:09:33.000Z",
  "updated": "2015-08-19T04:09:33.000Z",
  "title": "Nilpotent dessins: Decomposition theorem and classification of the abelian dessins",
  "authors": [
    "Kan Hu",
    "Roman Nedela",
    "Na-Er Wang"
  ],
  "comment": "27pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A map is a 2-cell decomposition of an orientable closed surface. A dessin is a bipartite map with a fixed colouring of vertices. A dessin is regular if its group of colour- and orientation-preserving automorphisms acts transitively on the edges, and a regular dessin is symmetric if it admits an additional external symmetry transposing the vertex colours. Regular dessins with nilpotent automorphism groups are investigated. We show that each such dessin is a parallel product of regular dessins whose automorphism groups are the Sylow subgroups. Regular and symmetric dessins with abelian automorphism groups are classified and enumerated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-19T04:09:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B25",
      "05C10"
    ],
    "keywords": [
      "decomposition theorem",
      "abelian dessins",
      "nilpotent dessins",
      "regular dessin",
      "classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150804523H"
    }
  }
}