On some metabelian 2-groups and applications I

• Autorzy: Abdelmalek Azizi , Abdelkader Zekhnini , Mohammed Taous
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 20D15: Nilpotent groups, p -groups
• 20D20: Sylow subgroups, Sylow properties, π -groups, π -structure
• 11R32: Galois theory
• 20E28: Maximal subgroups
• 11R20: Other abelian and metabelian extensions
• 11R11: Quadratic extensions
• 11R37: Class field theory
• 11R29: Class numbers, class groups, discriminants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 142
• Numer: 1
• Strony: 99-113

Daty

wydano

2016

Twórcy

autor

Abdelmalek Azizi

• Department of Mathematics, Faculty of Sciences, Mohammed First University, Oujda, Morocco

autor

Abdelkader Zekhnini

• Department of Mathematics, Polydisciplinary Faculty of Nador, Mohammed First University, Nador, Morocco

autor

Mohammed Taous

• Department of Mathematics, Faculty of Sciences and Technology, Moulay Ismail University, Errachidia, Morocco

Identyfikatory

DOI

10.4064/cm142-1-5