Isomorphism theorems for Galois groups of splitting fields of polynomials*

Victor Alexandru, Marian Vâjâitu, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)2185-2191
Number of pages7
JournalCommunications in Algebra
Volume47
Issue number5
DOIs
StatePublished - May 4 2019

Keywords

  • Diophantine approximation
  • Galois groups
  • polynomials
  • splitting fields

ASJC Scopus subject areas

  • Algebra and Number Theory

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