Notes on the ideal class groups of the p-class fields of some algebraic number fields

DOI10.3792/pjaa.68.79zbMath0762.11044OpenAlexW2093391652MaRDI QIDQ1201485

Katsuya Miyake

Publication date: 17 January 1993

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.68.79

zbMATH Keywords

\(p\)-rankideal class groupsabelian cubic fieldsHilbert \(p\)-class fieldrelative quadratic extensions

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Galois cohomology (11R34) Other abelian and metabelian extensions (11R20)

Related Items (1)

Notes on the existence of unramified non-abelian \(p\)-extensions over cyclic fields

Cites Work

• Algebraic investigations of Hilbert's theorem 94, the principal ideal theorem and the capitulation problem
• On the ideal class groups of the \(p\)-class fields of quadratic number fields
• Some \(p\)-groups with two generators which satisfy certain conditions arising from arithmetic in imaginary quadratic fields
• On the existence of unramified p-extensions
• Central extensions and Schur’s multiplicators of Galois groups
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