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

• Autores: Ali Mouhib, Abdelmalek Azizi
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 218, Nº 1, 2005, págs. 17-36
• Idioma: francés
• DOI: 10.2140/pjm.2005.218.17
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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)).