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.
@article{27016,
title = {On some metabelian 2-group and applications II},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {34},
year = {2015},
doi = {10.5269/bspm.v34i2.27016},
language = {EN},
url = {http://dml.mathdoc.fr/item/27016}
}
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed. On some metabelian 2-group and applications II. Boletim da Sociedade Paranaense de Matemática, Tome 34 (2015) . doi : 10.5269/bspm.v34i2.27016. http://gdmltest.u-ga.fr/item/27016/