English

Abstract

We study the capitulation of ideal classes in an infinite family of imaginary bicyclic biquadratic number fields consisting of fields k = Q( √ 2pq, i), where i = √ −1 and p ≡ −q ≡ 1 (mod 4) are different primes. For each of the three quadratic extensions K/k inside the absolute genus field k(∗) of k, we compute the capitulation kernel of K/k. Then we deduce that each strongly ambiguous class of k/Q(i) capitulates already in k(∗), which is smaller than the relative genus field (k/Q(i))∗.