{
  "id": "math/0504097",
  "version": "v3",
  "published": "2005-04-06T09:00:26.000Z",
  "updated": "2005-09-01T08:59:41.000Z",
  "title": "On Normal Subgroups of Product of Groups",
  "authors": [
    "Ashish Kumar Das"
  ],
  "comment": "5 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "The object of this paper is to find a necessary and sufficient condition for the groups $G_1, G_2, ..., G_n$ so that every normal subgroup of the product $\\prod_{i=1}^{n} G_i$ is of the type $\\prod_{i=1}^{n} N_i$ with $N_i \\trianglelefteq G_i$, $i=1,2, ..., n$. As a consequence we obtain a well-known result due to R. Remak about centreless completely reducible groups having finitely many direct factors.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-09-01T08:59:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D06",
      "20D40"
    ],
    "keywords": [
      "normal subgroup",
      "sufficient condition",
      "well-known result",
      "direct factors",
      "consequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4097D"
    }
  }
}