Kummer theory for number fields via entanglement groups

Antonella Perucca*, Pietro Sgobba, Sebastiano Tronto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let K be a number field, and let G be a finitely generated subgroup of K×. We are interested in computing the degree of the cyclotomic-Kummer extension K(Gn) over K, where Gn consists of all n-th roots of the elements of G. We develop the theory of entanglements introduced by Lenstra, and we apply it to compute the above degrees.

Original languageEnglish
Pages (from-to)251-270
Number of pages20
JournalManuscripta Mathematica
Issue number1-2
Publication statusPublished - Sept 2022
Externally publishedYes


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