{
  "id": "1411.0985",
  "version": "v1",
  "published": "2014-11-04T18:00:51.000Z",
  "updated": "2014-11-04T18:00:51.000Z",
  "title": "Finite morphic $p$-groups",
  "authors": [
    "A. Caranti",
    "C. M. Scoppola"
  ],
  "comment": "6 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "According to Li, Nicholson and Zan, a group $G$ is said to be morphic if, for every pair $N_{1}, N_{2}$ of normal subgroups, each of the conditions $G/N_{1} \\cong N_{2}$ and $G/N_{2} \\cong N_{1}$ implies the other. Finite, homocyclic $p$-groups are morphic, and so is the nonabelian group of order $p^{3}$ and exponent $p$, for $p$ an odd prime. In this paper we show that these are the only examples of finite, morphic $p$-groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-04T18:00:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15"
    ],
    "keywords": [
      "finite morphic",
      "normal subgroups",
      "nonabelian group",
      "odd prime",
      "homocyclic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.0985C"
    }
  }
}