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 $K[X]$ 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.

Keywords:

• Galois groups
• splitting fields
• polynomials
• Diophantine approximation

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 11R32
• 11S20
• 11J99

Disclosure statement

No potential conflict of interest was reported by the authors.