International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 767-771
doi:10.1155/S0161171292000991

Matrix powers over finite fields

Maria T. Acosta-De-Orozco1 and Javier Gomez-Calderon2

1Department of Mathematics, Penn State University, Beaver Campus, Monaca 15061, Pennsylvania, USA
2Department of Mathematics, Penn State University, New Kensington Campus, New Kensington 15068, Pennsylvania, USA

Received 23 May 1991; Revised 18 May 1992

Copyright © 1992 Maria T. Acosta-De-Orozco and Javier Gomez-Calderon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let GF(q) denote the finite field of order q=pe with p odd. Let M denote the ring of 2×2 matrices with entries in GF(q). Let n denote a divisor of q−1 and assume 2≤n and 4 does not divide n. In this paper, we consider the problem of determining the number of n-th roots in M of a matrix B∈M. Also, as a related problem, we consider the problem of lifting the solutions of X2=B over Galois rings.