Isomorphism theorems for Galois groups of splitting fields of polynomials*

Abstract

Let K be an arbitrary field of characteristic zero with an absolute value on it. We show that if F and G are monic and normal polynomials of of the same degree with coefficients close enough to each other with respect to this absolute value, then the Galois groups of the splitting fields of F and G over K are isomorphic. We point out a quantitative result and discuss some special cases and related problems.