On some metabelian 2-group and applications II-Reference-Cited by-同舟云学术

On some metabelian 2-group and applications II

Published:2015-06-29 Issue:2 Volume:34 Page:75-85
ISSN:2175-1188
Container-title:Boletim da Sociedade Paranaense de Matemática
language:en
Short-container-title:bspm

Author:

Azizi Abdelmalek¹^ORCID,Zekhnini Abdelkader¹^ORCID,Taous Mohammed²^ORCID

Affiliation:

1. Mohammed First University

2. Moulay Ismail University

Abstract

Let G be some metabelian 2-group satisfying the condition 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 field of k.

Publisher

Sociedade Paranaense de Matematica

Subject

General Mathematics

Reference15 articles.

1. 1. A. Azizi, A. Zekhnini and M. Taous, Coclass of Gal(k(2) 2 /k) for some fields k = Q..vp1p2q,v-1 with 2-class groups of type (2, 2, 2), to appear in J. Algebra Appl, (2015). DOI: 10.1142/S0219498816500274.

2. 2. A. Azizi, A. Zekhnini and M. Taous, Structure of Gal(k(2) 2 /k) for some fields k = Q(v2p1p2, i) with Cl2(k) . (2, 2, 2), Abh. Math. Sem. Univ. Hamburg, Volume 84, 2 (2014), 203-231.

3. 3. A. Azizi, A. Zekhnini, M. Taous and Daniel C. Mayer, Principalization of 2-class groups of type (2, 2, 2) of biquadratic fields Q(vp1p2q, i), Int. J. Number Theory, Vol. 11, No. 04, pp. 1177-1215 (2015).

4. 4. A. Azizi, A. Zekhnini and M. Taous, On some metabelian 2-group whose abelianization is of type (2, 2, 2) and applications, J. Taibah Univ. Sci. (2015), http://dx.doi.org/10.1016/j.jtusci.2015.01.007.

5. 5. A. Azizi, A. Zekhnini and M. Taous, On some metabelian 2-group and applications I, to appear in Colloquium Mathematicum.

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