Abstract

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 field of K. Let K₂⁽²⁾ be the Hilbert 2-class field of K₂⁽¹⁾ and K^(*) the genus field 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⁾).

Keywords

groupe de classes, capitulation, corps de classes de Hilbert

Mathematical Subject Classification

Primary: 11R27, 11R37

Authors