{
  "id": "1806.03774",
  "version": "v1",
  "published": "2018-06-11T02:25:47.000Z",
  "updated": "2018-06-11T02:25:47.000Z",
  "title": "Counting subgroups of fixed order in finite abelian groups",
  "authors": [
    "Fikreab Admasu",
    "Amit Sehgal"
  ],
  "comment": "18 pages. Comments welcome!",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We use recurrence relations to derive explicit formulas for counting the number of subgroups of given order (or index) in rank 3 finite abelian p-groups and use these to derive similar formulas in few cases for rank 4. As a consequence, we answer some questions by M. T$\\ddot{a}$rn$\\ddot{a}$uceanu in \\cite{MT} and L. T$\\dot{\\acute{o}}$th in \\cite{LT}. We also use other methods such as the method of fundamental group lattices introduced in \\cite{MT} to derive a similar counting function in a special case of arbitrary rank finite abelian p-groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-11T02:25:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite abelian groups",
      "fixed order",
      "counting subgroups",
      "arbitrary rank finite abelian p-groups",
      "fundamental group lattices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}