Abstract

Let K be a number field of class number one and let L be a tame cyclic extension of K of prime power degree. Put G = G(L/K) and pm = #G, where p is a prime number. Let K’ be a finite extension of K, containing the pm th roots of unity, which is disjoint from L over K and such that the . . . discrtmmants D,,, and D,,, are relatively prime. Put L’ = K’L and denote by A, A’, B, B’ the rings of integers in K, K’, L, L’, respectively. We will identify G with G(L’/K’) under the canonical isomorphism. The following result will be proved in this paper:

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