Abstract :
LetKbe a real abelian number field satisfying certain conditions andKnthenth layer of the cyclotomic imagep-extension ofK. We study the relations between thep-Sylow subgroup of the ideal class group and that of the unit group modulo the cyclotomic unit group ofKn. Supposing that Greenbergʹs conjecture is valid, we shall show that these two groups are isomorphic as Galois modules for sufficiently largen.
