{
  "id": "1303.1584",
  "version": "v1",
  "published": "2013-03-07T01:04:45.000Z",
  "updated": "2013-03-07T01:04:45.000Z",
  "title": "Conciseness of coprime commutators in finite groups",
  "authors": [
    "Cristina Acciarri",
    "Pavel Shumyatsky",
    "Anitha Thillaisundaram"
  ],
  "comment": "7 pages",
  "doi": "10.1017/S0004972713000361",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group. We show that the order of the subgroup generated by coprime $\\gamma_k$-commutators (respectively $\\delta_k$-commutators) is bounded in terms of the size of the set of coprime $\\gamma_k$-commutators (respectively $\\delta_k$-commutators). This is in parallel with the classical theorem due to Turner-Smith that the words $\\gamma_k$ and $\\delta_k$ are concise.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-07T01:04:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D25",
      "20F12"
    ],
    "keywords": [
      "finite group",
      "coprime commutators",
      "conciseness",
      "classical theorem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.1584A"
    }
  }
}