 For each "x" in "A" that is not in the center, the centralizer "Zx" of "x" is clearly a skew-field and thus a field, by the induction hypothesis, and because "Zx" can be viewed as a vector space over "Z"("A") and "A" can be viewed as a vector space over "Zx", we have that "Zx" has order "qd" where "d" divides "n" and is less than "n".Viewing "Z"("A")*, "A*", and the "Z*x" as groups under multiplication, we can write the class equation
where the sum is taken over the conjugacy classes not contained within "Z"("A")*, and the "d" are defined so that for each conjugacy class, the order of "Z*x" for any "x" in the class is "qd"-1.