{
  "id": "1811.10025",
  "version": "v1",
  "published": "2018-11-25T14:46:41.000Z",
  "updated": "2018-11-25T14:46:41.000Z",
  "title": "Coprime commutators in finite groups",
  "authors": [
    "Carmine Monetta",
    "Raimundo Bastos"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group and let $k \\geq 2$. We prove that the coprime subgroup $\\gamma_k^*(G)$ is nilpotent if and only if $|xy|=|x||y|$ for any $\\gamma_k^*$-commutators $x,y \\in G$ of coprime orders (Theorem A). Moreover, we show that the coprime subgroup $\\delta_k^*(G)$ is nilpotent if and only if $|ab|=|a||b|$ for any powers of $\\delta_k^*$-commutators $a,b\\in G$ of coprime orders (Theorem B).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-25T14:46:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "coprime commutators",
      "coprime subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}