On some metabelian 2-groups and applications I

Abdelmalek Azizi, Abdelkader Zekhnini, and Mohammed Taous. "On some metabelian 2-groups and applications I." Colloquium Mathematicae 142.1 (2016): 99-113. <http://eudml.org/doc/283866>.

@article{AbdelmalekAzizi2016,
abstract = {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 $Gal(k₂^\{(2)\}/k) ≃ G$, where $k₂^\{(2)\}$ is the second Hilbert 2-class field of k.},
author = {Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous},
journal = {Colloquium Mathematicae},
language = {eng},
number = {1},
pages = {99-113},
title = {On some metabelian 2-groups and applications I},
url = {http://eudml.org/doc/283866},
volume = {142},
year = {2016},
}

TY - JOUR
AU - Abdelmalek Azizi
AU - Abdelkader Zekhnini
AU - Mohammed Taous
TI - On some metabelian 2-groups and applications I
JO - Colloquium Mathematicae
PY - 2016
VL - 142
IS - 1
SP - 99
EP - 113
AB - 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 $Gal(k₂^{(2)}/k) ≃ G$, where $k₂^{(2)}$ is the second Hilbert 2-class field of k.
LA - eng
UR - http://eudml.org/doc/283866
ER -