{
  "id": "2312.07907",
  "version": "v1",
  "published": "2023-12-13T05:25:59.000Z",
  "updated": "2023-12-13T05:25:59.000Z",
  "title": "On recognition of the direct squares of the simple groups with abelian Sylow 2-subgroups",
  "authors": [
    "Tao Li",
    "A. R. Moghaddamfar",
    "Andrey V. Vasil'ev",
    "Zhigang Wang"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "The spectrum of a group is the set of orders of its elements. Finite groups with the same spectra as the direct squares of the finite simple groups with abelian Sylow 2-subgroups are considered. It is proved that the direct square $J_1\\times J_1$ of the sporadic Janko group $J_1$ and the direct squares ${^2}G_2(q)\\times{^2}G_2(q)$ of the simple small Ree groups ${^2}G_2(q)$ are uniquely characterized by their spectra in the class of finite groups, while for the direct square $PSL_2(q)\\times PSL_2(q)$ of a 2-dimensional simple linear group $PSL_2(q)$, there are always infinitely many groups (even solvable groups) with the same spectra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-13T05:25:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D60",
      "20D06"
    ],
    "keywords": [
      "direct square",
      "abelian sylow",
      "finite groups",
      "recognition",
      "simple small ree groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}