{
  "id": "2003.06072",
  "version": "v1",
  "published": "2020-03-13T00:38:24.000Z",
  "updated": "2020-03-13T00:38:24.000Z",
  "title": "A result on the number of cyclic subgroups of a finite group",
  "authors": [
    "Marius Tărnăuceanu"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group and $\\alpha(G)=\\frac{|C(G)|}{|G|}$\\,, where $C(G)$ denotes the set of cyclic subgroups of $G$. In this short note, we prove that $\\alpha(G)\\leq\\alpha(Z(G))$ and we describe the groups $G$ for which the equality occurs. This gives some sufficient conditions for a finite group to be $4$-abelian or abelian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-13T00:38:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "cyclic subgroups",
      "sufficient conditions",
      "equality occurs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}