{
  "id": "1805.12411",
  "version": "v1",
  "published": "2018-05-31T10:30:13.000Z",
  "updated": "2018-05-31T10:30:13.000Z",
  "title": "Engel groups with an identity",
  "authors": [
    "Pavel Shumyatsky",
    "Antonio Tortora",
    "Maria Tota"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We give an affrmative answer to the question whether a residually finite Engel group satisfying an identity is locally nilpotent. More generally, for a residually finite group G with an identity, we prove that the set of right Engel elements of G is contained in the Hirsch-Plotkin radical of G. Given an arbitrary word w, we also show that the class of all groups G in which the w-values are right n-Engel and w(G) is locally nilpotent is a variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-31T10:30:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F45",
      "20E26",
      "20F40"
    ],
    "keywords": [
      "locally nilpotent",
      "right engel elements",
      "right n-engel",
      "residually finite engel group satisfying",
      "arbitrary word"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}