{
  "id": "math/9703201",
  "version": "v1",
  "published": "1997-03-10T22:26:04.000Z",
  "updated": "1997-03-10T22:26:04.000Z",
  "title": "Maximal subgroups of direct products",
  "authors": [
    "Jacques Thévenaz"
  ],
  "comment": "Plain TeX file, 8 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We determine all maximal subgroups of the direct product $\\sc G^n$ of $\\sc n$ copies of a group~$\\sc G$. If $\\sc G$ is finite, we show that the number of maximal subgroups of~$\\sc G^n$ is a quadratic function of~$\\sc n$ if $\\sc G$ is perfect, but grows exponentially otherwise. We~deduce a theorem of Wiegold about the growth behaviour of the number of generators of~$\\sc G^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-03-10T22:26:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximal subgroups",
      "direct product",
      "quadratic function",
      "growth behaviour",
      "generators"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997math......3201T"
    }
  }
}