Algebraic investigations of Hilbert's theorem 94, the principal ideal theorem and the capitulation problem

zbMath0704.11048MaRDI QIDQ916713

Katsuya Miyake

Publication date: 1989

Published in: Expositiones Mathematicae (Search for Journal in Brave)

zbMATH Keywords

ideal class groupsclass field theoryunramified abelian extensionsPrincipal Ideal Theoremregular p-groupsArtin's splitting modulecapitulation generaCapitulation ProblemHerbrand's LemmaHilbert's Theorem 94transfers of finite groups

Mathematics Subject Classification ID

Class field theory (11R37) Class numbers, class groups, discriminants (11R29) Other abelian and metabelian extensions (11R20)

Related Items (18)

Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions ⋮ Sur une question de capitulation ⋮ On some metabelian 2-groups and applications III ⋮ On the 2-class field tower of some imaginary biquadratic number fields ⋮ Imaginary quadratic fields \(k\) with cyclic \(\text{Cl}_2(k^1)\) ⋮ The distribution of second \(p\)-class groups on coclass graphs ⋮ On the metacyclic 2-groups whose abelianizations are of type \((2, 2^n)\), \(n\geq 2\) and applications ⋮ Transfers of metabelian \(p\)-groups ⋮ On the rank of the 2-class group of \(\mathbb Q(\sqrt{p},\sqrt{q},\sqrt{-1})\) ⋮ On the ideal class groups of the \(p\)-class fields of quadratic number fields ⋮ Notes on the ideal class groups of the p-class fields of some algebraic number fields ⋮ Some \(p\)-groups with two generators which satisfy certain conditions arising from arithmetic in imaginary quadratic fields ⋮ Group Theory and the Capitulation Problem for Some Number Fields ⋮ Capitulation and transfer kernels ⋮ The works of Claude Chevalley on class field theory: an introduction ⋮ On the maximal unramified pro-2-extension of certain cyclotomic \(\mathbb{Z}_2\)-extensions ⋮ On the 2-class field towers of some imaginary quartic cyclic number fields ⋮ Unnamed Item

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