Let K be a real abelian number field satisfying certain conditions andKnthenth layer of the cyclotomic p-extension ofK. We study the relation between the p-Sylow subgroup of the ideal class group and that of the unit group module the cyclotomic unit group ofKn. We give certain sufficient conditions which assure that the above two groups are isomorphic as Galois modules for sufficiently largen. We shall also show that they have the same p-rank for sufficiently largen.
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