{
  "id": "1901.04774",
  "version": "v1",
  "published": "2019-01-15T11:40:33.000Z",
  "updated": "2019-01-15T11:40:33.000Z",
  "title": "Profinite groups with restricted centralizers of commutators",
  "authors": [
    "E. Detomi",
    "M. Morigi",
    "P. Shumyatsky"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "A group G has restricted centralizers if for each g in G the centralizer C_G(g) either is finite or has finite index in G. A theorem of Shalev states that a profinite group with restricted centralizers is abelian-by-finite. In the present article we handle profinite groups with restricted centralizers of word-values. We show that if w is a multilinear commutator word and G a profinite group with restricted centralizers of w-values, then the verbal subgroup w(G) is abelian-by-finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-15T11:40:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F24",
      "20E18",
      "20F12"
    ],
    "keywords": [
      "restricted centralizers",
      "handle profinite groups",
      "multilinear commutator word",
      "finite index",
      "shalev states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}