{
  "id": "2005.13929",
  "version": "v1",
  "published": "2020-05-28T11:49:07.000Z",
  "updated": "2020-05-28T11:49:07.000Z",
  "title": "Commutators and commutator subgroups of finite $p$-groups",
  "authors": [
    "Rahul Kaushik",
    "Manoj K. Yadav"
  ],
  "comment": "23 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We present a classification of finite $p$-groups $G$, $p \\ge 3$, with $\\gamma_2(G)$, the commutator subgroup of $G$, of order $p^4$ and exponent $p$ such that each element of $\\gamma_2(G)$ is a commutator. As a consequence, it follows that for any $p$-group $G$ of order at least $p^9$, $p \\ge 5$, with $|\\gamma_2(G)| = p^4$, every element of $\\gamma_2(G)$ is a commutator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-28T11:49:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15",
      "20F12"
    ],
    "keywords": [
      "commutator subgroup",
      "classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}