Serre, Jean-Pierre 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 Cited in 2 ReviewsCited in 2 Documents 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 Citations:Zbl 0659.00006 PDFBibTeX XML Full Text: Numdam EuDML