{
  "id": "2103.04102",
  "version": "v1",
  "published": "2021-03-06T11:33:31.000Z",
  "updated": "2021-03-06T11:33:31.000Z",
  "title": "On the rank of a verbal subgroup of a finite group",
  "authors": [
    "Eloisa Detomi",
    "Marta Morigi",
    "Pavel Shumyatsky"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:0911.3048",
  "categories": [
    "math.GR"
  ],
  "abstract": "We show that if $w$ is a multilinear commutator word and $G$ a finite group in which every metanilpotent subgroup generated by $w$-values is of rank at most $r$, then the rank of the verbal subgroup $w(G)$ is bounded in terms of $r$ and $w$ only. In the case where $G$ is soluble we obtain a better result -- if $G$ is a finite soluble group in which every nilpotent subgroup generated by $w$-values is of rank at most $r$, then the rank of $w(G)$ is at most $r+1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-06T11:33:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D20",
      "20F12"
    ],
    "keywords": [
      "verbal subgroup",
      "finite group",
      "multilinear commutator word",
      "better result",
      "finite soluble group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}