{
  "id": "1208.3046",
  "version": "v3",
  "published": "2012-08-15T07:15:50.000Z",
  "updated": "2013-05-17T02:22:19.000Z",
  "title": "On finite $p$-groups whose central automorphisms are all class preserving",
  "authors": [
    "Manoj K. Yadav"
  ],
  "comment": "12 pages, Accepted for publication in Comm. Algebra, A minor modification is done in the proof of Proposition 3.4 to make it work for all primes (including 2)",
  "categories": [
    "math.GR"
  ],
  "abstract": "We obtain certain results on a finite $p$-group whose central automorphisms are all class preserving. In particular, we prove that if $G$ is a finite $p$-group whose central automorphisms are all class preserving, then $d(G)$ is even, where $d(G)$ denotes the number of elements in any minimal generating set for $G$. As an application of these results, we obtain some results regarding finite $p$-groups whose automorphisms are all class preserving. In particular, we prove that if $G$ is a finite $p$-groups whose automorphisms are all class preserving, then order of $G$ is at least $p^8$ and the order of the automorphism group of $G$ is at least $p^12$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-05-17T02:22:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D45",
      "20D15"
    ],
    "keywords": [
      "class preserving",
      "central automorphisms",
      "automorphism group",
      "results regarding finite",
      "minimal generating set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.3046Y"
    }
  }
}