On the regular semisimple elements and primary classes of GL(n,q)

The present paper deals with counting the number and orders of regular semisimple elements, together with the number of primary classes of GL(n,q). The approach used in this paper depends essentially on partitions of positive integers ⩽n. We give the numbers of regular semisimple elements and primary classes of GL(n,q) for n∈{1,2,…,6} and see that the number of regular semisimple elements is an integral polynomial in q, while the number of primary classes is a rational polynomial in q.