{
  "id": "2003.14057",
  "version": "v1",
  "published": "2020-03-31T09:48:45.000Z",
  "updated": "2020-03-31T09:48:45.000Z",
  "title": "Generating functions for the powers in $\\text{GL}(n,q)$",
  "authors": [
    "Rijubrata Kundu",
    "Anupam Singh"
  ],
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "Consider the set of all powers $\\text{GL}(n ,q)^M = \\{x^M \\mid x\\in \\text{GL}(n, q)\\}$ for an integer $M\\geq 2$. In this article, we aim to enumerate the regular, regular semisimple and semisimple elements as well as conjugacy classes in the set $\\text{GL}(n, q)^M$, i.e., the elements or classes of these kinds which are $M^{th}$ powers. We get the generating functions for (i) regular and regular semisimple elements (and classes) when $(q,M)=1$, (ii) for semisimple elements and all elements (and classes) when $M$ is a prime power and $(q,M)=1$, and (iii) for all kinds when $M$ is a prime and $q$ is a power of $M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-31T09:48:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G40"
    ],
    "keywords": [
      "generating functions",
      "regular semisimple elements",
      "prime power",
      "conjugacy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}