Kummer theory for number fields via entanglement groups

English

Perucca, Antonella[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Sgobba, Pietro[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Tronto, Sebastiano[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Undated

No

[en] Number fields ; Kummer theory ; Degree ; Radical extensions

[en] Let $K$ be a number field, and let $G$ be a finitely generated and torsion-free subgroup of $K^\times$. We are interested in computing the degree of the cyclotomic-Kummer extension $K(\sqrt[n]{G})$ over $K$, where $\sqrt[n]{G}$ consists of all $n$-th roots of the elements of $G$. We develop the theory of entanglements introduced by Lenstra, and apply it to compute the above degrees.