Construction of normal bases for absolute Galois extensions with quaternionic Galois group of order 12

DOI10.5802/jtnb.348zbMath1069.11046OpenAlexW2316460388MaRDI QIDQ1396434

Jacques Queyrut, Jean Cougnard

Publication date: 30 June 2003

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2002__14_1_87_0

zbMATH Keywords

quaternion groupfiber productnormal basisring of integersstably free

Mathematics Subject Classification ID

Galois theory (11R32) Separable extensions, Galois theory (12F10) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

Related Items (2)

Computing generators of free modules over orders in group algebras. ⋮ Normal integral bases for 𝐴₄ extensions of the rationals

Uses Software

• PARI/GP

Cites Work

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• Galois module structure and rootnumbers for quaternion extensions of degree \(2^ n\).
• Sur l'arithmétique des extensions galoisiennes à groupe de Galois diédral d'ordre \(2p\)
• Projective modules over binary polyhedral groups.
• Simplification pour les ordres des corps de quaternions totalement définis.
• Arithmetic and Galois module structure for tame extensions.
• Modules sur l'algèbre du groupe quaternionien
• Introduction to Algebraic K-Theory. (AM-72)
• Construction of a normal basis for extensions of \(\mathbb Q\) with group \(D_4\)

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