International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 767-771
Matrix powers over finite fields
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.
Let denote the finite field of order with odd. Let denote the ring of matrices with entries in . Let denote a divisor of and assume and does not divide . In this paper, we consider the problem of determining the number of -th roots in of a matrix . Also, as a related problem, we consider the problem of lifting the solutions of over Galois rings.