{
  "id": "1707.09652",
  "version": "v1",
  "published": "2017-07-30T17:53:40.000Z",
  "updated": "2017-07-30T17:53:40.000Z",
  "title": "Choosing elements from finite fields",
  "authors": [
    "Michael Vaughan-Lee"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "In two important papers from 1960 Graham Higman introduced the notion of PORC functions, and he proved that for any given positive integer $n$ the number of $p$-class two groups of order $p^n$ is a PORC function of $p$. A key result in his proof of this theorem is the following: \"The number of ways of choosing a finite number of elements from the finite field of order $q^n$ subject to a finite number of monomial equations and inequalities between them and their conjugates over GF($q$), considered as a function of $q$, is PORC.\" Higman's proof of this result involves five pages of homological algebra. Here we give a short elementary proof of the result. Our proof is constructive, and gives an algorithms for computing the relevant PORC functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-30T17:53:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "choosing elements",
      "finite number",
      "short elementary proof",
      "relevant porc functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}