{
  "id": "2409.11591",
  "version": "v1",
  "published": "2024-09-17T22:50:06.000Z",
  "updated": "2024-09-17T22:50:06.000Z",
  "title": "On $G$-character tables for normal subgroups",
  "authors": [
    "María José Felipe",
    "María Dolores Pérez-Ramos",
    "Víctor Sotomayor"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $N$ be a normal subgroup of a finite group $G$. From a result due to Brauer, it can be derived that the character table of $G$ contains square submatrices which are induced by the $G$-conjugacy classes of elements in $N$ and the $G$-orbits of irreducible characters of $N$. In the present paper, we provide an alternative approach to this fact through the structure of the group algebra. We also show that such matrices are non-singular and become a useful tool to obtain information of $N$ from the character table of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-17T22:50:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20E45",
      "20C05"
    ],
    "keywords": [
      "normal subgroup",
      "character table",
      "contains square submatrices",
      "finite group",
      "conjugacy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}