TY - JOUR

T1 - Scalar polynomial functions on the nonsingular matrices over a finite field

AU - Brawley, Joel V.

AU - Mullen, Gary L.

N1 - Funding Information:
*E-mail: [email protected] 'E-mail:M [email protected] %l. 1s author would like to thank the Mathematical Sciences Department University for its hospitality during his sabbatical when this paper was written. The also thanks the NSA for partial support under grant agreement MDA904-87-H-2023.

PY - 1992/9

Y1 - 1992/9

N2 - 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.

AB - 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.

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U2 - 10.1016/0024-3795(92)90037-B

DO - 10.1016/0024-3795(92)90037-B

M3 - Article

AN - SCOPUS:44049112931

SN - 0024-3795

VL - 174

SP - 1

EP - 12

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -