Published online by Cambridge University Press: 22 January 2016
In this paper we shall prove the following theorem conjectured by Miyake in [3] (see also Jaulent [2]).
THEOREM. Let k be a finite algebraic number field and K be an unramified abelian extension of k, then all ideals belonging to at least [K: k] ideal classes of k become principal in K.
Since the capitulation homomorphism is equivalently translated to a group-transfer of the galois group (see Miyake [3]), it is enough to prove the following group-theoretical verison:
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