{
  "id": "1704.01746",
  "version": "v1",
  "published": "2017-04-06T08:27:17.000Z",
  "updated": "2017-04-06T08:27:17.000Z",
  "title": "The Nilpotency Criterion for the Derived Subgroup of a Finite Group",
  "authors": [
    "Victor S. Monakhov"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "It is proved that the derived subgroup of a finite group is nilpotent if and only if $|ab|\\ge |a||b|$ for all primary commutators $a$ and $b$ of coprime orders.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-06T08:27:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "derived subgroup",
      "nilpotency criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}