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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

##### MSC:
 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
##### Keywords:
inverse problem of Galois theory; bibliographies
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