{
  "id": "1506.00143",
  "version": "v1",
  "published": "2015-05-30T17:25:10.000Z",
  "updated": "2015-05-30T17:25:10.000Z",
  "title": "Finite generation of iterated wreath products in product action",
  "authors": [
    "Matteo Vannacci"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $\\mathcal{S}$ be a sequence of finite perfect transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated wreath product in product action of the groups in $\\mathcal{S}$ is topologically finitely generated, provided that the actions of the groups in $\\mathcal{S}$ are not regular. We prove that our bound has the right asymptotic behaviour. We also deduce that other infinitely iterated mixed wreath products of groups in $\\mathcal{S}$ are finitely generated. Finally we apply our methods to find explicitly two generators of infinitely iterated wreath products in product action of special sequences $\\mathcal{S}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-30T17:25:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E18",
      "20F05",
      "20B05",
      "20E22"
    ],
    "keywords": [
      "product action",
      "finite generation",
      "infinitely iterated wreath product",
      "iterated mixed wreath products",
      "finite perfect transitive permutation groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150600143V"
    }
  }
}