{
  "id": "0909.4393",
  "version": "v1",
  "published": "2009-09-24T09:13:53.000Z",
  "updated": "2009-09-24T09:13:53.000Z",
  "title": "On triple factorisations of finite groups",
  "authors": [
    "S. Hassan Alavi",
    "Cheryl E. Praeger"
  ],
  "comment": "28 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "This paper introduces and develops a general framework for studying triple factorisations of the form $G=ABA$ of finite groups $G$, with $A$ and $B$ subgroups of $G$. We call such a factorisation nondegenerate if $G\\neq AB$. Consideration of the action of $G$ by right multiplication on the right cosets of $B$ leads to a nontrivial upper bound for $|G|$ by applying results about subsets of restricted movement. For $A<C<G$ and $B<D<G$ the factorisation $G=CDC$ may be degenerate even if $G=ABA$ is nondegenerate. Similarly forming quotients may lead to degenerate triple factorisations. A rationale is given for reducing the study of nondegenerate triple factorisations to those in which $G$ acts faithfully and primitively on the cosets of $A$. This involves study of a wreath product construction for triple factorisations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-24T09:13:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B05",
      "20B15",
      "20D40"
    ],
    "keywords": [
      "finite groups",
      "nondegenerate triple factorisations",
      "nontrivial upper bound",
      "wreath product construction",
      "studying triple factorisations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4393H"
    }
  }
}