アルティン・ハッセの指数関数
This gives a third proof that the coefficients of "E"("x") are "p"-integral, using the theorem of Frobenius that in a finite group of order divisible by "d" the number of elements of order dividing "d" is also divisible by "d". Apply this theorem to the "n"th symmetric group with "d" equal to the highest power of "p" dividing "n"!.