The inverse Galois problem is to determine, for a given field K and a given finite group G, whether there exists a Galois extension of K, whose Galois group is isomorphic to G. And if there is such an extension, to find an explicit polynomial over K, whose Galois group is the prescribed group G. The authors present a family of “generic” polynomials for certain finite groups, which give all Galois extensions having the required group as their Galois group. The existence of such generic polynomials is discussed and a detailed treatment of their construction is given in those cases, when they exist.

Reviewer:

jtu