{
  "id": "2406.04559",
  "version": "v1",
  "published": "2024-06-07T00:26:36.000Z",
  "updated": "2024-06-07T00:26:36.000Z",
  "title": "The automorphism groups of small affine rank 3 graphs",
  "authors": [
    "Jin Guo",
    "Andrey V. Vasil'ev",
    "Rui Wang"
  ],
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "A rank 3 graph is an orbital graph of a rank 3 permutation group of even order. Despite the classification of rank 3 graphs being complete, see, e.g., Chapter 11 of the recent monograph 'Strongly regular graphs' by Brouwer and Van Maldeghem, the full automorphism groups of these graphs (equivalently, the 2-closures of rank 3 groups) have not been explicitly described, though a lot of information on this subject is available. In the present note, we address this problem for the affine rank 3 graphs. We find the automorphism groups for finitely many relatively small graphs and show that modulo known results, this provides the full description of the automorphism groups of the affine rank 3 graphs, thus reducing the general problem to the case when the socle of the automorphism group is nonabelian simple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-07T00:26:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B25",
      "05E18",
      "05E30"
    ],
    "keywords": [
      "small affine rank",
      "monograph strongly regular graphs",
      "full automorphism groups",
      "permutation group",
      "nonabelian simple"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}