Commutators in finite simple groups of Lie type

Using properties of the Steinberg character, we obtain a congruence module p for the number of ways in which a p-regular element may be expressed as a commutator in a finite simple group G of Lie type of characteristic p. Thi s congruence shows that such an element is a commutator in G. We also show that if K and L are conjugacy classes of G consisting of elements whose cen tralizers have order relatively prime to p, then any p-regular element of G is expressible as the product of an element of K and an element of L.