Classification of metabelian 2-groups \(G\) with \(\mathbf{G}^{\mathrm{ab}} (\mathbf{2},\mathbf{2}^{\mathbf n})\), \(\mathbf n\geq \mathbf 2\), and rank \(\mathbf d(\mathbf G^{\prime})=\mathbf 2\). Applications to real quadratic number fields
From MaRDI portal
Publication:1672020
DOI10.1016/J.JPAA.2018.03.004zbMath1435.11139OpenAlexW2795201391MaRDI QIDQ1672020
Publication date: 7 September 2018
Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jpaa.2018.03.004
Class field theory (11R37) Class numbers, class groups, discriminants (11R29) Finite nilpotent groups, (p)-groups (20D15)
Related Items (3)
On the metacyclic 2-groups whose abelianizations are of type \((2, 2^n)\), \(n\geq 2\) and applications ⋮ On the Hilbert 2-class field of some quadratic number fields ⋮ The narrow 2-class field tower of some real quadratic number fields
Cites Work
- Real quadratic fields with abelian 2-class field tower
- Imaginary quadratic fields \(k\) with cyclic \(\text{Cl}_2(k^1)\)
- Corrigendum to: ``Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group.
- Some real quadratic number fields whose Hilbert 2-class fields have class number congruent to 2 modulo 4
- Über Den Bizyklischen Biquadratischen Zahlkörper
- Kuroda's class number formula
- On the rank of the 2-class group of the Hilbert 2-class field of some quadratic fields
- Imaginary quadratic fields \(k\) with \(\text{Cl}_ 2(k)\simeq(2,2^ m)\) and rank \(\text{Cl}_ 2(k^ 1)=2\).
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Classification of metabelian 2-groups \(G\) with \(\mathbf{G}^{\mathrm{ab}} (\mathbf{2},\mathbf{2}^{\mathbf n})\), \(\mathbf n\geq \mathbf 2\), and rank \(\mathbf d(\mathbf G^{\prime})=\mathbf 2\). Applications to real quadratic number fields
