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Groupes de Galois sur \({\mathbb{Q}}\). (Galois groups over \({\mathbb{Q}})\). (French) Zbl 0684.12009
Sémin. Bourbaki, 40ème Année, Vol. 1987/88, Exp. No. 689, Astérisque 161/162, 73-85 (1988).
[For the entire collection see Zbl 0659.00006.]
The classical problem whether for a given finite group G there exists a finite Galois extension E over the rational number field \({\mathbb{Q}}\) such that the Galois group Gal(E/\({\mathbb{Q}})\) is isomorphic to G is not completely solved yet. However, there are many groups for which the problem has a positive answer. For this problem, the author gives in this paper a comprehensive research survey with abundant examples and many bibliographies.
Reviewer: H.Yokoi

11R32 Galois theory
12F10 Separable extensions, Galois theory
20F29 Representations of groups as automorphism groups of algebraic systems
12-02 Research exposition (monographs, survey articles) pertaining to field theory
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