The degree of Kummer extensions of number fields

Antonella Perucca, Pietro Sgobba*, Sebastiano Tronto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Let K be a number field, and let α1,.,αr be elements of K× which generate a subgroup of K× of rank r. Consider the cyclotomic-Kummer extensions of K given by K(ζn,α1n1,.,αrnr), where ni divides n for all i. There is an integer x such that these extensions have maximal degree over K(ζg,α1g1,.,αrgr), where g =gcd(n,x) and gi =gcd(ni,x). We prove that the constant x is computable. This result reduces to finitely many cases the computation of the degrees of the extensions K(ζn,α1n1,.,αrnr) over K.

Original languageEnglish
Pages (from-to)1091-1110
Number of pages20
JournalInternational Journal of Number Theory
Issue number5
Publication statusPublished - Jun 2021
Externally publishedYes


  • Kummer extension
  • Kummer theory
  • Number field
  • degree


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