Perissinotto, Flavio[University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]

Perucca, Antonella[University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]

Undated

No

[en] Kummer theory ; Finite fields ; p-adic fields

[en] Let K be a finite field or a finite extension of Qp for some prime number p. If G is a finitely generated subgroup of K*, then we can consider the degree of the cyclotomic-Kummer extension K(\zeta_N, \sqrt[n]{G})/K, where n divides N. If K is a finite field, then we give a closed formula for the degree, while if K is a p-adic field, then we describe a strategy to compute the degree.