{
  "id": "1211.1797",
  "version": "v3",
  "published": "2012-11-08T09:19:31.000Z",
  "updated": "2014-10-26T09:05:39.000Z",
  "title": "Representing and counting the subgroups of the group Z_m x Z_n",
  "authors": [
    "Mario Hampejs",
    "Nicki Holighaus",
    "László Tóth",
    "Christoph Wiesmeyr"
  ],
  "comment": "12 pages, 1 figure, revised",
  "journal": "Journal of Numbers, Volume 2014, Article ID 491428",
  "categories": [
    "math.GR",
    "math.CO",
    "math.NT"
  ],
  "abstract": "We deduce a simple representation and the invariant factor decompositions of the subgroups of the group $\\Bbb{Z}_m \\times \\Bbb{Z}_n$, where $m$ and $n$ are arbitrary positive integers. We obtain formulas for the total number of subgroups and the number of subgroups of a given order.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-03T10:49:18.000Z",
      "title": "On the subgroups of the group Z_m x Z_n",
      "abstract": "We deduce a simple representation and the invariant factor decompositions of the subgroups of the group Z_m x Z_n, where m and n are arbitrary positive integers. We obtain formulas for the total number of subgroups and the number of subgroups of a given order.",
      "comment": "12 pages, 1 figure, revised, the invariant factor decompositions of the subgroups are also given",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-26T09:05:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20K01",
      "20K27",
      "05A15",
      "11A25"
    ],
    "keywords": [
      "invariant factor decompositions",
      "total number",
      "simple representation",
      "arbitrary positive integers"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.1797H"
    }
  }
}