{
  "id": "1505.04468",
  "version": "v1",
  "published": "2015-05-17T22:14:33.000Z",
  "updated": "2015-05-17T22:14:33.000Z",
  "title": "On residually finite groups with Engel-like conditions",
  "authors": [
    "Raimundo Bastos"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $m,n$ be positive integers. Suppose that $G$ is a residually finite group in which for every element $x \\in G$ there exists a positive integer $q=q(x) \\leqslant m$ such that $x^q$ is $n$-Engel. We show that $G$ is locally virtually nilpotent. Further, let $w$ be a multilinear commutator and $G$ a residually finite group in which for every product of at most $896$ $w$-values $x$ there exists a positive integer $q=q(x)$ dividing $m$ such that $x^q$ is $n$-Engel. Then $w(G)$ is locally virtually nilpotent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-17T22:14:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F45",
      "20E26"
    ],
    "keywords": [
      "residually finite group",
      "engel-like conditions",
      "positive integer",
      "locally virtually nilpotent",
      "multilinear commutator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150504468B"
    }
  }
}