International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 2, Pages 279-287
A note of equivalence classes of matrices over a finite field
1Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, USA
2Department of Mathematics, The Pennsylvania State University, Sharon, Pennsylvania, USA
Received 16 July 1980
Copyright © 1981 J. V. Brawley and 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 algebra of matrices over the finite field of elements, and let denote a group of permutations of . It is well known that each can be represented uniquely by a polynomial of degree less than ; thus, the group naturally determines a relation on as follows: if then if for some . Here is to be interpreted as substitution into the unique polynomial of degree which represents .
In an earlier paper by the second author , it is assumed that the relation is an equivalence relation and, based on this assumption, various properties of the relation are derived. However, if , the relation is not an equivalence relation on . It is the purpose of this paper to point out the above erroneous assumption, and to discuss two ways in which hypotheses of the earlier paper can be modified so that the results derived there are valid.