{
  "id": "2312.16416",
  "version": "v1",
  "published": "2023-12-27T05:27:44.000Z",
  "updated": "2023-12-27T05:27:44.000Z",
  "title": "A Proof of Gross' Conjecture on $2$-Automorphic $2$-Groups",
  "authors": [
    "Cai Heng Li",
    "Yan Zhou Zhu"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Building upon previous results, a classification is given of finite $p$-groups of which subgroups of order $p$ are all fused. This completes the classification problem dated back to Higman 1963 on the so-called Suzuki $2$-groups, and confirms a conjecture of Gross proposed in 1974. As a consequence, two open problems on AT-groups and FIF-groups are solved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-27T05:27:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "automorphic",
      "classification problem",
      "open problems",
      "fif-groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}