{
  "id": "1707.04187",
  "version": "v1",
  "published": "2017-07-13T15:53:51.000Z",
  "updated": "2017-07-13T15:53:51.000Z",
  "title": "Finite groups with Engel sinks of bounded rank",
  "authors": [
    "E. I. Khukhro",
    "P. Shumyatsky"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "For an element $g$ of a group $G$, an Engel sink is a subset ${\\mathscr E}(g)$ such that for every $x\\in G$ all sufficiently long commutators $[...[[x,g],g],\\dots ,g]$ belong to ${\\mathscr E}(g)$. A~finite group is nilpotent if and only if every element has a trivial Engel sink. We prove that if in a finite group $G$ every element has an Engel sink generating a subgroup of rank~$r$, then $G$ has a normal subgroup $N$ of rank bounded in terms of $r$ such that $G/N$ is nilpotent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-13T15:53:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "bounded rank",
      "trivial engel sink",
      "sufficiently long commutators",
      "normal subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}