Nombre de $\varphi$-classes invariantes. Application aux classes des corps abéliens
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Publication:4173460
DOI10.24033/bsmf.1876zbMath0392.12005OpenAlexW2585465640MaRDI QIDQ4173460
Publication date: 1978
Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=BSMF_1978__106__337_0
cyclic extensionabelian extensionStickelberger theoremSylow groupl-adic charactersubgroup of Galois group
Galois theory (11R32) Class numbers, class groups, discriminants (11R29) Other abelian and metabelian extensions (11R20)
Related Items (7)
New relative extension examples without normal basis ⋮ Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions ⋮ Unités et classes dans les extensions metabéliennes de degrè \(n\ell^s\) sur un corps de nombres algébriques ⋮ \(p\)-adic approach of Greenberg's conjecture for totally real fields ⋮ The Chevalley-Herbrand formula and the real abelian Main Conjecture (new criterion using capitulation of the class group) ⋮ On the structure of relative class groups. With an appendix of numerical examples ⋮ Relative normal bases in some cyclotomic extensions
Cites Work
- Signature des unités cyclotomiques et parité du nombre de classes des extensions cycliques de \(Q\) de degré premier impair
- Classes d'idéaux des corps abéliens et nombres de Bernoulli généralisés
- A modular construction of unramified p-extensions of \(\mathbb{Q}(\mu_p)\)
- On a cubic field with discriminant \(163^2\)
- On divisibility by 2 of the relative class numbers of imaginary number fields
- Critère de parité du nombre de classes des extensions abéliennes réelles de $Q$ de degré impair
- Unit signatures, and even class numbers, and relative class numbers.
- Relation entre les 2-groupes des classes d'idéaux au sens ordinaire et restreint de certains corps de nombres
- Onp-adicL-functions and cyclotomic fields. II
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