On the capitulation of the $2$-ideal classes of the field Q(\sqrt{pq_1q_2}, i) of type (2, 2, 2)

Résumé

We study the capitulation of the 2-ideal classes of the field k =Q(\sqrt{p_1p_2q}, \sqrt{-1}), where p_1\equiv p_2\equiv-q\equiv1 \pmod 4  are different primes, in its three quadratic extensions contained in its absolute genus field k^{*} whenever the 2-class group of $\kk$ is of type $(2, 2, 2)$.