On the capitulation of the $2$-ideal classes of the field Q(\sqrt{pq_1q_2}, i) of type (2, 2, 2)-Reference-Cited by-同舟云学术

On the capitulation of the $2$-ideal classes of the field Q(\sqrt{pq_1q_2}, i) of type (2, 2, 2)

Published:2019-03-10 Issue:4 Volume:38 Page:127-135
ISSN:2175-1188
Container-title:Boletim da Sociedade Paranaense de Matemática
language:
Short-container-title:B Soc Paran Mat

Author:

Azizi Abdelmalek^ORCID,Zekhnini Abdelkader^ORCID,Taous Mohammed^ORCID

Abstract

We study the capitulation of the 2-ideal classes of the field k =Q(\sqrt{p_1p_2q}, \sqrt{-1}), where p_1\equiv p_2\equiv-q\equiv1 \pmod 4 are different primes, in its three quadratic extensions contained in its absolute genus field k^{*} whenever the 2-class group of $\kk$ is of type $(2, 2, 2)$.

Publisher

Sociedade Paranaense de Matematica

Subject

General Mathematics

Reference12 articles.

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3. 3. A. Azizi and M. Taous, Determination des corps k = Q(vd,v-1) dont les 2-groupes de classes sont de type (2, 4) ou (2, 2, 2), Rend. Istit. Mat. Univ. Trieste. 40 (2008), 93-116, Zbl 1215.11107, MR2583453.

4. On the generators of the 2-class group of the field k = Q(vd, i);Azizi;IJPAM,2012

5. 5. A. Azizi, A. Zekhnini and M. Taous, On the strongly ambiguous classes of k/Q(i) where k = Q(v2p1p2, i), Asian-Eur. J. Math. 7 (2014), no. 1, Zbl 1292.11119, MR3189588.

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