INVERSE GALOIS PROBLEM WITH VIEWPOINT TO GALOIS THEORY AND IT’S APPLICATIONS

mathematics

In this paper we are presenting a review of the inverse Galois Problem and its applications. In mathematics, more specifically in abstract algebra, Galois Theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois Theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood. Originally, Galois used permutation groups to describe how the various roots of a given polynomial equation are related to each other. Galois Theory is the algebraic study of groups that can be associated with polynomial equations. In this survey we outline the milestones of the Inverse Problem of Galois theory historically up to the present time. We summarize as well the contribution of the authors to the Galois Embedding Problem, which is the most natural approach to the Inverse Problem in the case of non-simple groups.

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.