Abdelmalek Azizi

Capitulation of the 2-ideal classes of Q(√d, i)

Let d ∈ 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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