{
  "id": "1304.2961",
  "version": "v1",
  "published": "2013-04-10T13:50:23.000Z",
  "updated": "2013-04-10T13:50:23.000Z",
  "title": "On the subgroups of finite Abelian groups of rank three",
  "authors": [
    "Mario Hampejs",
    "László Tóth"
  ],
  "comment": "11 pages, 3 tables",
  "journal": "Annales Univ. Sci. Budapest., Sect. Comp. 39 (2013), 111-124",
  "categories": [
    "math.GR",
    "math.NT"
  ],
  "abstract": "We describe the subgroups of the group $\\Z_m \\times \\Z_n \\times \\Z_r$ and derive a simple formula for the total number $s(m,n,r)$ of the subgroups, where $m,n,r$ are arbitrary positive integers. An asymptotic formula for the function $n\\mapsto s(n,n,n)$ is also deduced.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-10T13:50:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20K01",
      "20K27",
      "11A25",
      "11N37"
    ],
    "keywords": [
      "finite abelian groups",
      "asymptotic formula",
      "simple formula",
      "arbitrary positive integers",
      "total number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.2961H"
    }
  }
}