{
  "id": "1611.03302",
  "version": "v1",
  "published": "2016-11-10T14:00:43.000Z",
  "updated": "2016-11-10T14:00:43.000Z",
  "title": "The number of subgroups of the group $\\Bbb{Z}_m\\times \\Bbb{Z}_n \\times \\Bbb{Z}_r \\times \\Bbb{Z}_s$",
  "authors": [
    "László Tóth"
  ],
  "comment": "13 pages, tables",
  "categories": [
    "math.GR",
    "math.CO",
    "math.NT"
  ],
  "abstract": "We deduce direct formulas for the total number of subgroups and the number of subgroups of a given order of the group $\\Bbb{Z}_m\\times \\Bbb{Z}_n \\times \\Bbb{Z}_r \\times \\Bbb{Z}_s$, where $m,n,r,s\\in \\Bbb{N}$. The proofs are by some simple group theoretical and number theoretical arguments based on Goursat's lemma for groups. Two conjectures are also formulated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-10T14:00:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20K01",
      "20K27",
      "11A25",
      "11Y70"
    ],
    "keywords": [
      "deduce direct formulas",
      "total number",
      "number theoretical arguments",
      "goursats lemma",
      "conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}