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 Zp-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 Zp-torsion subgroup of the odd part of the
Galois group Gal(N ∩ L∕k∞) is isomorphic, over the group ring Zp[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∞).
