International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 503-512
Permutation matrices and matrix equivalence over a finite field
Department of Mathematics, The Pennsylvania State University, Sharon 16146, Pennsylvania, USA
Received 21 March 1980; Revised 12 August 1980
Copyright © 1981 Gary L. Mullen. 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 and the ring of matrices over . Let be the set of all permutation matrices of order over so that is ismorphic to . If is a subgroup of and , then is equivalent to relative to if there exists such that . In sections 3 and 4, if formulas are given for the number of equivalence classes of a given order and for the total number of classes. In sections 5 and 6 we study two generalizations of the above definition.