{
  "id": "1703.00979",
  "version": "v1",
  "published": "2017-03-02T22:59:50.000Z",
  "updated": "2017-03-02T22:59:50.000Z",
  "title": "On verbal subgroups in finite and profinite groups",
  "authors": [
    "Cristina Acciarri",
    "Pavel Shumyatsky"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1112.5879",
  "journal": "Algebra Discrete Math., 14 (2012), 1--13",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $w$ be a multilinear commutator word. In the present paper we describe recent results that show that if $G$ is a profinite group in which all $w$-values are contained in a union of finitely (or in some cases countably) many subgroups with a prescribed property, then the verbal subgroup $w(G)$ has the same property as well. In particular, we show this in the case where the subgroups are periodic or of finite rank.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-02T22:59:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E18",
      "20F14"
    ],
    "keywords": [
      "profinite group",
      "verbal subgroup",
      "multilinear commutator word",
      "finite rank",
      "prescribed property"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}