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We study the capitulation of 2-ideal classes of an infinite family of imaginary biquadratic number fields consisting of fields =ℚ(pq1q2,i)$\mathbb {k} =\mathbb {Q}(\sqrt {pq_{1}q_{2}}, i)$, where i=−1$i=\sqrt {-1}$ and q1≡q2≡−p≡−1 (mod 4) are different primes. For each of the three quadratic extensions K/$\mathbb {K}/\mathbb {k}$ inside the absolute genus field (∗) of , we compute the capitulation kernel of K/$\mathbb {K}/\mathbb {k}$. Then we deduce that each strongly ambiguous class of /ℚ(i)$\mathbb {k}/\mathbb {Q}(i)$ capitulates already in (∗).

Capitulation in the Absolutely Abelian Extensions of some Number Fields II