  Let G be a cyclic p-group of order p^n acting by automorphisms on a
(non-necessarily commutative) ring R. Suppose there is an element x in R such
that (1 + t + ... + t^{p-1})(x) = 1, where t is an element of order p in G. We
show how to construct an element y in R such that (1 + s + ... + s^{p^n-1})(y)
= 1, where s is a generator of G.
