{
  "id": "1908.07030",
  "version": "v1",
  "published": "2019-08-19T19:09:06.000Z",
  "updated": "2019-08-19T19:09:06.000Z",
  "title": "Normal Subgroups of Powerful $p$ -groups",
  "authors": [
    "James Williams"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this note we show that if $p$ is an odd prime and $G$ is a powerful $p$-group with $N\\leq G^{p}$ and $N$ normal in $G$, then $N$ is powerfully nilpotent. An analogous result is proved for $p=2$ when $N\\leq G^{4}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-19T19:09:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15"
    ],
    "keywords": [
      "normal subgroups",
      "odd prime",
      "powerfully nilpotent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}