Scalar polynomial functions on the nonsingular matrices over a finite field

Joel V. Brawley, Gary L. Mullen

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Let F = Fq denote the finite field of order q, and let GLn = GL(n, q) denote the general linear group of all nonsingular n × n matrices over F. A function f : GLn → GLn is called a scalar polynomial function on GLn if there exists a polynomial f(x) ε{lunate} F[x] which, when considered as a matrix function under substitution, represents the function tf. In this paper we characterize those polynomials f(x) ε{lunate} F[x] which define scalar polynomial functions on GLn and we characterize those polynomials f(x) which determine permutations of GLn. Also we enumerate both the functions and the permutations of GLn which are scalar polynomial functions.

Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalLinear Algebra and Its Applications
Volume174
Issue numberC
DOIs
StatePublished - Sep 1992

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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