Abdelmalek Azizi

Sur la capitulation des 2 classes d’Idéaux de Q (\ sqrt {d}, i).

Let d ε N, i = √−1, k = Q (√d, i), k1 be the 2-Hilbert class field of k, k2 the 2-Hilbert class field of k1, Ck, 2 the 2-component of the class group of k and G2 the Galois group of k2/k. We suppose that the group Ck, 2 is of type (2, 2); then k1 contains three extensions Fi/k, i = 1, 2, 3. The aim of this Note is to study the problem of capitulation of the 2-ideal classes of k in Fi, i = 1, 2, 3, and to determine the structure of G2.

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