{
  "id": "2203.12704",
  "version": "v1",
  "published": "2022-03-23T19:54:57.000Z",
  "updated": "2022-03-23T19:54:57.000Z",
  "title": "The Average of Some Irreducible Character Degrees",
  "authors": [
    "Ramadan Elsharif",
    "Mark L. Lewis"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We are interested in determining the bound of the average of the degrees of the irreducible characters whose degrees are not divisible by some prime $p$ that guarantees a finite group $G$ of odd order is $p$-nilpotent. We find a bound that depends on the prime $p$. If we further restrict our average by fixing a subfield $k$ of the complex numbers and then compute the average of the degrees of the irreducible characters whose degrees are not divisible by $p$ and have values in $k$, then we will see that we obtain a bound that depends on both $p$ and $k$. Moreover, we find examples that make those bounds best possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-23T19:54:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15"
    ],
    "keywords": [
      "irreducible character degrees",
      "finite group",
      "odd order",
      "complex numbers",
      "bounds best"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}