{
  "id": "2007.00967",
  "version": "v1",
  "published": "2020-07-02T08:57:16.000Z",
  "updated": "2020-07-02T08:57:16.000Z",
  "title": "On the number of $p$-elements in a finite group",
  "authors": [
    "Pietro Gheri"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this paper we study the ratio between the number of $p$-elements and the order of a Sylow $p$-subgroup of a finite group $G$. As well known, this ratio is a positive integer and we conjecture that, for every group $G$, it is at least the $(1-\\frac{1}{p})$-th power of the number of Sylow $p$-subgroups of $G$. We prove this conjecture if $G$ is $p$-solvable. Moreover, we prove that the conjecture is true in its generality if a somewhat similar condition holds for every almost simple group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-02T08:57:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "somewhat similar condition holds",
      "conjecture",
      "simple group",
      "th power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}