Let G be some metabelian 2-group satisfying the condition G/G’ ≃ ℤ/2ℤ × ℤ/2ℤ × ℤ/2ℤ. 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 for the 2-ideal classes of some fields k satisfying the condition , where is the second Hilbert 2-class field of k.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-1-5,
author = {Abdelmalek Azizi and Abdelkader Zekhnini and Mohammed Taous},
title = {On some metabelian 2-groups and applications I},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {99-113},
zbl = {06497301},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-1-5}
}
Abdelmalek Azizi; Abdelkader Zekhnini; Mohammed Taous. On some metabelian 2-groups and applications I. Colloquium Mathematicae, Tome 144 (2016) pp. 99-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-1-5/