{
  "id": "2009.13590",
  "version": "v1",
  "published": "2020-09-28T19:10:31.000Z",
  "updated": "2020-09-28T19:10:31.000Z",
  "title": "Finding Supercharacter Theories on Character Tables",
  "authors": [
    "Frieder Ladisch"
  ],
  "comment": "18 pages, ancillary file with GAP code",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We describe an easy way how to find supercharacter theories for a finite group $G$, if the character table of $G$ is known. Namely, we show how an arbitrary partition of the conjugacy classes of $G$ or of the irreducible characters of $G$ can be refined to the coarsest partition that belongs to a supercharacter theory. Our constructions emphasize the duality between superclasses and supercharacters. An algorithm is presented to find all supercharacter theories on a given character table. The algorithm is used to compute the number of supercharacter theories for some nonabelian simple groups with up to 26 conjugacy classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-28T19:10:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15"
    ],
    "keywords": [
      "supercharacter theory",
      "finding supercharacter theories",
      "character table",
      "conjugacy classes",
      "nonabelian simple groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}