{
  "id": "1309.5219",
  "version": "v1",
  "published": "2013-09-20T09:37:39.000Z",
  "updated": "2013-09-20T09:37:39.000Z",
  "title": "Regular dessins with a given automorphism group",
  "authors": [
    "Gareth A. Jones"
  ],
  "comment": "19 pages",
  "categories": [
    "math.GR",
    "math.AG"
  ],
  "abstract": "Dessins d'enfants are combinatorial structures on compact Riemann surfaces defined over algebraic number fields, and regular dessins are the most symmetric of them. If G is a finite group, there are only finitely many regular dessins with automorphism group G. It is shown how to enumerate them, how to represent them all as quotients of a single regular dessin U(G), and how certain hypermap operations act on them. For example, if G is a cyclic group of order n then U(G) is a map on the Fermat curve of degree n and genus (n-1)(n-2)/2. On the other hand, if G=A_5 then U(G) has genus 274218830047232000000000000000001. For other non-abelian finite simple groups, the genus is much larger.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-20T09:37:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H57",
      "14H37",
      "20B25",
      "30F10"
    ],
    "keywords": [
      "automorphism group",
      "non-abelian finite simple groups",
      "compact riemann surfaces",
      "algebraic number fields",
      "hypermap operations act"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.5219J"
    }
  }
}