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.
Disclosure statement
No potential conflict of interest was reported by the authors.