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Let K = Q(,), where d1 and d2 are positive square-free integers such that (d1,d2) = 1. Let K2(1) be the Hilbert 2-class ?eld of K. Let K2(2) be the Hilbert 2-class ?eld of K2(1) and K(*) the genus ?eld of K. We suppose that K2(1)K(*) and Gal(K2(1)/K) ? Z/2Z × Z/2Z. We study the capitulation problem of the 2-ideal classes of K in the sub-extensions of K2(1)/K and we determine the structure of Gal(K2(2)).

Capitulation des 2-classes d’idéaux de certains corps biquadratiques dont le corps de genres diffère du 2-corps de classes de Hilbert