{
  "id": "2001.07275",
  "version": "v1",
  "published": "2020-01-20T22:56:22.000Z",
  "updated": "2020-01-20T22:56:22.000Z",
  "title": "A generalization of a result on the sum of element orders of a finite group",
  "authors": [
    "Marius Tărnăuceanu"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group and let $\\psi(G)$ denote the sum of element orders of $G$. It is well-known that the maximum value of $\\varphi$ on the set of groups of order $n$, where $n$ is a positive integer, will occur at the cyclic group $C_n$. For nilpotent groups, we prove a natural generalization of this result, obtained by replacing the element orders of $G$ with the element orders relative to a certain subgroup $H$ of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-20T22:56:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "maximum value",
      "cyclic group",
      "nilpotent groups",
      "natural generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}