{
  "id": "1808.00253",
  "version": "v1",
  "published": "2018-08-01T10:29:48.000Z",
  "updated": "2018-08-01T10:29:48.000Z",
  "title": "A Criterion for Solvability of a Finite Group by the Sum of Element Orders",
  "authors": [
    "Morteza Baniasad Azad",
    "Behrooz Khosravi"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group and $\\psi(G) = \\sum_{g \\in G} o(g)$, where $o(g)$ denotes the order of $g \\in G$. In [M. Herzog, et. al., Two new criteria for solvability of finite groups, J. Algebra, 2018], the authors put forward the following conjecture: \\textbf{Conjecture.} \\textit{If $G$ is a group of order $n$ and $\\psi(G)>211\\psi(C_n)/1617 $, where $C_n$ is the cyclic group of order $n$, then $G$ is solvable.} In this paper we prove the validity of this conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-01T10:29:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "element orders",
      "solvability",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}