{
  "id": "1807.08238",
  "version": "v1",
  "published": "2018-07-22T06:02:03.000Z",
  "updated": "2018-07-22T06:02:03.000Z",
  "title": "Bounding the number of characters in a block of a finite group",
  "authors": [
    "Benjamin Sambale"
  ],
  "comment": "16 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We present a strong upper bound on the number k(B) of irreducible characters of a p-block B of a finite group G in terms of local invariants. More precisely, the bound depends on a chosen major B-subsection (u,b), its normalizer N_G(\\langle u\\rangle,b) in the fusion system and a weighted sum of the Cartan invariants of b. In this way we strengthen and unify previous bounds given by Brauer, Wada, K\\\"ulshammer--Wada, H\\'ethelyi--K\\\"ulshammer--Sambale and the present author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-22T06:02:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "strong upper bound",
      "chosen major b-subsection",
      "local invariants",
      "cartan invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}