{
  "id": "1910.07686",
  "version": "v1",
  "published": "2019-10-17T02:47:34.000Z",
  "updated": "2019-10-17T02:47:34.000Z",
  "title": "Critical group structure from the parameters of a strongly regular graph",
  "authors": [
    "Joshua E. Ducey",
    "David L. Duncan",
    "Wesley J. Engelbrecht",
    "Jawahar V. Madan",
    "Eric Piato",
    "Christina S. Shatford",
    "Angela Vichitbandha"
  ],
  "comment": "20 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give simple arithmetic conditions that force the Sylow $p$-subgroup of the critical group of a strongly regular graph to take a specific form. These conditions depend only on the parameters $(v, k, \\lambda, \\mu)$ of the strongly regular graph under consideration. We give many examples, including how the theory can be used to compute the critical group of Conway's $99$-graph and to give an elementary argument that no $srg(28,9,0,4)$ exists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-17T02:47:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "strongly regular graph",
      "critical group structure",
      "parameters",
      "simple arithmetic conditions",
      "specific form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}