On a quotient of the unramified Iwasawa module over an abelian number field, II

Let p be an odd prime number, k an imaginary abelian field containing a primitive p-th root of unity, and k(infinity)/k the cyclotomic Z(p)-extension. Denote by L/k(infinity) the maximal unramified pro p abelian extension, and by L the maximal intermediate field of L/k(infinity) in which all prime divisors of k(infinity) over p split completely. Let N/k(infinity) ( resp. N'/k(infinity)) be the pro-p abelian extension generated by all p-power roots of all units (resp. p-units) of k(infinity). In the previous paper, we proved that the Z(p)-torsion subgroup of the odd part of the Galois group Gal(N boolean AND L/k(infinity)) 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(infinity). In this paper, we prove that the same holds also for the Galois group Gal(N'boolean AND L'/ k(infinity)).