{
  "id": "2306.02390",
  "version": "v1",
  "published": "2023-06-04T15:48:18.000Z",
  "updated": "2023-06-04T15:48:18.000Z",
  "title": "The $(2,3)$-generation of the finite simple orthogonal groups, I",
  "authors": [
    "M. A. Pellegrini",
    "M. C. Tamburini Bellani"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "The complete classification of the finite simple groups that are $(2,3)$-generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$-generators for the finite odd-dimensional orthogonal groups $\\Omega_{2k+1}(q)$ with $q$ odd and $k\\geq 4$. As a byproduct we also obtain $(2,3)$-generators for $\\Omega_{4k}^+(q)$ with $k\\geq 3$ and $q$ odd, and for $\\Omega_{4k+2}^\\pm(q)$ with $k\\geq 4$ and $q\\equiv \\pm 1 \\pmod 4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-04T15:48:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G40"
    ],
    "keywords": [
      "finite simple orthogonal groups",
      "finite odd-dimensional orthogonal groups",
      "generation",
      "finite simple groups",
      "generators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}