{
  "id": "1911.13284",
  "version": "v1",
  "published": "2019-11-29T18:36:54.000Z",
  "updated": "2019-11-29T18:36:54.000Z",
  "title": "On the diameters of McKay graphs for finite simple groups",
  "authors": [
    "Martin W. Liebeck",
    "Aner Shalev",
    "Pham Huu Tiep"
  ],
  "categories": [
    "math.GR",
    "math.RT"
  ],
  "abstract": "Let $G$ be a finite group, and $\\alpha$ a nontrivial character of $G$. The McKay graph ${\\mathcal M}(G,\\alpha)$ has the irreducible characters of $G$ as vertices, with an edge from $\\chi_1$ to $\\chi_2$ if $\\chi_2$ is a constituent of $\\alpha\\chi_1$. We study the diameters of McKay graphs for simple groups $G$. For $G$ a group of Lie type, we show that for any $\\alpha$, the diameter is bounded by a quadratic function of the rank, and obtain much stronger bounds for $G={\\rm PSL}_n(q)$ or ${\\rm PSU}_n(q)$. We also bound the diameter for symmetric and alternating groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-29T18:36:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20C30",
      "20C33"
    ],
    "keywords": [
      "finite simple groups",
      "mckay graph",
      "nontrivial character",
      "finite group",
      "lie type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}