{
  "id": "1702.02293",
  "version": "v1",
  "published": "2017-02-08T05:34:09.000Z",
  "updated": "2017-02-08T05:34:09.000Z",
  "title": "Finite $p$-groups with non-cyclic center have non-inner automorphism of order $p$",
  "authors": [
    "Rohit Garg",
    "Deepak Gumber"
  ],
  "comment": "3 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite non-abelian $p$-group. A longstanding conjecture asserts that $G$ admits a non-inner automorphism of order $p$. We confirm the conjecture in case $Z(G)$ is not cyclic. As a consequence, we also find necessary and sufficient conditions on $G$ such that the group of all central automorphisms of $G$ is minimal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-08T05:34:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15",
      "20D45"
    ],
    "keywords": [
      "non-inner automorphism",
      "non-cyclic center",
      "central automorphisms",
      "sufficient conditions",
      "longstanding conjecture asserts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}