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