A FORMAL DERIVATION ON INTEGRAL GROUP RINGS FOR CYCLIC GROUPS

Let G be a cyclic group of prime power order p(k), and let I be the augmentation ideal of the integral group ring Z[G]. We define a derivation on Z/p(k)Z[G], and show that for 2 <= n <= p, an element alpha is an element of I is in I-n if and only if the i-th derivative of the image of alpha in Z/p(k)Z[G] vanishes for 1 <= i <= (n -1).