{
  "id": "2202.13737",
  "version": "v1",
  "published": "2022-02-28T13:06:15.000Z",
  "updated": "2022-02-28T13:06:15.000Z",
  "title": "The Engel graph of a finite group",
  "authors": [
    "Eloisa Detomi",
    "Andrea Lucchini",
    "Daniele Nemmi"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "For a finite group $G,$ we investigate the direct graph $\\Gamma(G),$ whose vertices are the non-hypercentral elements of $G$ and where there is an edge $x\\mapsto y$ if and only if $[x,_ny]=1$ for some $n \\in \\mathbb N.$ We prove that $\\Gamma(G)$ is always weakly connected and is strongly connected if $G/Z_{\\infty}(G)$ is neither Frobenius nor almost simple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-28T13:06:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "engel graph",
      "non-hypercentral elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}