{
  "id": "1301.4093",
  "version": "v1",
  "published": "2013-01-17T13:36:10.000Z",
  "updated": "2013-01-17T13:36:10.000Z",
  "title": "Bounding the Exponent of a Verbal Subgroup",
  "authors": [
    "Eloisa Detomi",
    "Marta Morigi",
    "Pavel Shumyatsky"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We deal with the following conjecture. If w is a group word and G is a finite group in which any nilpotent subgroup generated by w-values has exponent dividing e, then the exponent of the verbal subgroup w(G) is bounded in terms of e and w only. We show that this is true in the case where w is either the nth Engel word or the word [x^n,y_1,y_2,...,y_k] (Theorem A). Further, we show that for any positive integer e there exists a number k=k(e) such that if w is a word and G is a finite group in which any nilpotent subgroup generated by products of k values of the word w has exponent dividing e, then the exponent of the verbal subgroup w(G) is bounded in terms of e and w only (Theorem B).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-17T13:36:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F10",
      "20F45",
      "20F14"
    ],
    "keywords": [
      "verbal subgroup",
      "finite group",
      "nilpotent subgroup",
      "nth engel word",
      "group word"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.4093D"
    }
  }
}