{
  "id": "1805.00301",
  "version": "v1",
  "published": "2018-05-01T12:58:36.000Z",
  "updated": "2018-05-01T12:58:36.000Z",
  "title": "A note on the number of cyclic subgroups of a finite group",
  "authors": [
    "Marius Tărnăuceanu",
    "Mihai-Silviu Lazorec"
  ],
  "comment": "13 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group, $L_1(G)$ be its poset of cyclic subgroups and consider the quantity $\\alpha(G)=\\frac{|L_1(G)|}{|G|}$. The aim of this paper is to study the class $\\cal{C}$ of finite nilpotent groups having $\\alpha(G)=\\frac{3}{4}$. We show that if $G$ belongs to this class, then it is a 2-group satisfying certain conditions. Also, we study the appartenance of some classes of finite groups to $\\cal{C}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-01T12:58:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "cyclic subgroups",
      "finite nilpotent groups",
      "appartenance",
      "conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}