Group Theory and the Capitulation Problem for Some Number Fields
From MaRDI portal
Publication:5738729
DOI10.1007/978-3-319-32902-4_1zbMath1417.11151OpenAlexW2556364245MaRDI QIDQ5738729
Mohammed Taous, Abdelkader Zekhnini, Abdelmalek Azizi
Publication date: 12 June 2017
Published in: Non-Associative and Non-Commutative Algebra and Operator Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-319-32902-4_1
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Algebraic investigations of Hilbert's theorem 94, the principal ideal theorem and the capitulation problem
- Number fields with class number congruent to 4 mod 8 and Hilbert's Theorem 94
- Principal ideal theorems in the genus field for absolutely abelian extensions
- Real quadratic fields with abelian 2-class field tower
- On the 2-class group of \(\mathbb{Q}(\sqrt{d},i)\)
- On 2-class field towers of some imaginary quadratic number fields
- Imaginary quadratic fields with \(Cl_2(k)\simeq (2,2,2)\).
- Construction of the 2-Hilbert class field tower of some biquadratic fields
- Imaginary bicyclic biquadratic fields with cyclic 2-class group
- Structure of \(\mathrm {Gal}(\Bbbk _2^{(2)}/\Bbbk)\) for some fields \(\Bbbk=\mathbb {Q}(\sqrt{2p_1p_2},i)\) with \(\mathbf {C}l_2(\Bbbk)\simeq (2, 2, 2)\)
- A principal ideal theorem in the genus field
- Sur le rang du 2-groupe de classes de ๐({โ{๐}},{โ{๐}}) oรน ๐=2 ou un premier ๐โก1(๐๐๐4)
- Coclass of ${\rm Gal}({\mathbb K}_2^{(2)}/{\mathbb K})$ for some fields ${\mathbb K} = {\mathbb Q}(\sqrt{p_1p_2q}, \sqrt{-1})$ with 2-class groups of types (2, 2, 2)
- On the $2$-groups whose abelianizations are of type $(2, 4)$ and applications
- Ideal class groups of cyclotomic number fields I
- Principalization of 2-class groups of type (2, 2, 2) of biquadratic fields ${\mathbb Q}(\sqrt{p_1p_2q}, \sqrt{-1})$
- Capitulation des 2-classes d'idรฉaux de k=Q (\sqrt 2p, i)
This page was built for publication: Group Theory and the Capitulation Problem for Some Number Fields