{
  "id": "2009.10121",
  "version": "v1",
  "published": "2020-09-21T18:24:30.000Z",
  "updated": "2020-09-21T18:24:30.000Z",
  "title": "On finiteness of verbal subgroups",
  "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 $G_w$. The word $w$ is concise if $w(G)$ is finite for all groups $G$ in which $G_w$ is finite. We obtain several results supporting the conjecture that the word $[u_1,\\dots,u_s]$ is concise whenever the words $u_1,\\dots,u_s$ are non-commutator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-21T18:24:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "verbal subgroup",
      "finiteness",
      "group-word"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}