{
  "id": "1811.04563",
  "version": "v1",
  "published": "2018-11-12T05:36:22.000Z",
  "updated": "2018-11-12T05:36:22.000Z",
  "title": "The number of cyclic subgroups of finite abelian groups and Menon's identity",
  "authors": [
    "Marius Tărnăuceanu"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this note, we give a new formula for the number of cyclic subgroups of a finite abelian group. This is based on applying the Burnside's lemma to a certain group action. Also, it generalizes the well-known Menon's identity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-12T05:36:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite abelian group",
      "cyclic subgroups",
      "well-known menons identity",
      "group action",
      "burnsides lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}