{
  "id": "1312.1485",
  "version": "v2",
  "published": "2013-12-05T09:56:15.000Z",
  "updated": "2014-09-23T07:49:45.000Z",
  "title": "Subgroups of finite Abelian groups having rank two via Goursat's lemma",
  "authors": [
    "László Tóth"
  ],
  "comment": "9 pages, revised, new results added, 1 figure, 1 table",
  "categories": [
    "math.GR",
    "math.CO",
    "math.NT"
  ],
  "abstract": "Using Goursat's lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Z_m x Z_n are deduced, where m and n are arbitrary positive integers. As consequences, explicit formulas for the total number of subgroups, the number of subgroups with a given invariant factor decomposition, and the number of subgroups of a given order are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-05T09:56:15.000Z",
      "abstract": "Using Goursat's lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Z_m x Z_n is deduced, where m and n are arbitrary positive integers. As consequences, explicit formulas for the total number of subgroups, number of cyclic subgroups and the number of subgroups of a given order are obtained.",
      "comment": "7 pages, 1 figure",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-23T07:49:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20K01",
      "20K27",
      "11A25"
    ],
    "keywords": [
      "finite abelian groups",
      "goursats lemma",
      "invariant factor decompositions",
      "total number",
      "cyclic subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.1485T"
    }
  }
}