Matzat, B. H. Über das Umkehrproblem der Galoisschen Theorie. (On the inverse problem of Galois theory). (German) Zbl 0662.12008 Jahresber. Dtsch. Math.-Ver. 90, No. 4, 155-183 (1988). Let K be a field, f(x)\(\in K[x]\) a polynomial. Then to f(x) is associated a group: if E is a splitting field for f(x) over K then Gal(E/K) is the group associated to f(x) called the Galois group of f(x) over K. The inverse problem of Galois theory for K is: Given a finite group G does there exist a polynomial f(x)\(\in K[x]\) such that the Galois group of f(x) over K is isomorphic to G? - The problem for \(K={\mathbb{Q}}\) is still open inspite of contributions by giants for 150 years. The author gives an excellent survey of the status of the problem. Reviewer: T.Soundararajan Cited in 4 ReviewsCited in 7 Documents MSC: 11R32 Galois theory 12-03 History of field theory 12F10 Separable extensions, Galois theory Keywords:inverse problem of Galois theory × Cite Format Result Cite Review PDF