Nombre de $\varphi$-classes invariantes. Application aux classes des corps abéliens

DOI10.24033/bsmf.1876zbMath0392.12005OpenAlexW2585465640MaRDI QIDQ4173460

Georges Gras

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

zbMATH Keywords

cyclic extensionabelian extensionStickelberger theoremSylow groupl-adic charactersubgroup of Galois group

Mathematics Subject Classification ID

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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