%0 Journal Article
%T On the strongly ambiguous classes of some biquadratic number fields
%A Abdelmalek Azizi
%A Abdelkader Zekhnini
%A Mohammed Taous
%J Mathematics
%D 2015
%I arXiv
%X We study the capitulation of ideal classes in an infinite family of imaginary bicyclic biquadratic number fields consisting of fields $k =Q(\sqrt{2pq}, i)$, where $i=\sqrt{-1}$ and $p\equiv -q\equiv1 \pmod 4$ 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 $\left(k/Q(i)\right)^*$.
%U http://arxiv.org/abs/1503.01992v1