{
  "id": "2009.11775",
  "version": "v1",
  "published": "2020-09-24T16:04:26.000Z",
  "updated": "2020-09-24T16:04:26.000Z",
  "title": "On finiteness of some verbal subgroups in profinite groups",
  "authors": [
    "João Azevedo",
    "Pavel Shumyatsky"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Given a group word $w$ and a group $G$, the set of $w$-values in $G$ is denoted by $G_w$ and the verbal subgroup $w(G)$ is the one generated by $G_w$. In the present paper we consider profinite groups admitting a word $w$ such that the cardinality of $G_w$ is less than $2^{\\aleph_0}$ and $w(G)$ is generated by finitely many $w$-values. For several families of words $w$ we show that under these assumptions $w(G)$ must be finite. Our results are related to the concept of conciseness of group words.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-24T16:04:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "verbal subgroup",
      "finiteness",
      "group word",
      "conciseness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}