Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous

On some metabelian 2-group and applications II

Let G be some metabelian 2-group such that G/G’ is of type (2, 2, 2). In this paper, we construct all the subgroups of G of index 2 or 4, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem of the 2-ideal classes of some �fields k satisfying the condition Gal(k_2^2/k) is isomorphic to G, where k_2^2 is the second Hilbert 2-class �eld of k.

Accéder au lien