Abstract

Let p be an odd prime number, k an imaginary abelian field containing a primitive p-th root of unity, and k_∞ ∕ k the cyclotomic Z_p-extension. Denote by L ∕ k_∞ the maximal unramified pro–p abelian extension, and by L′ the maximal intermediate field of L ∕ k_∞ in which all prime divisors of k_∞ over p split completely. Let N ∕ k_∞ (resp. N′ ∕ k_∞) be the pro–p abelian extension generated by all p-power roots of all units (resp. p-units) of k_∞. In the previous paper, we proved that the Z_p-torsion subgroup of the odd part of the Galois group Gal(N ∩ L ∕ k_∞) is isomorphic, over the group ring Z_p[Gal(k ∕ Q)], to a certain standard subquotient of the even part of the ideal class group of k_∞. In this paper, we prove that the same holds also for the Galois group Gal(N′∩ L′ ∕ k_∞).

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