Families of Sextic Number Fields with Prescribed Indices

Hamid Bouaouina; Lhoussain El Fadil; Omar  Kchit; Bouchaïb  Sodaïgui

doi:10.5269/bspm.81060

Families of Sextic Number Fields with Prescribed Indices

Hamid Bouaouina Faculty of Sciences Dhar El Mahraz, P.O. Box 1796 Atlas-Fes, Sidi Mohamed ben Abdellah University, Morocco and Université Polytechnique Hauts-de-France Ceramaths FR, CNRS 2037F-59313 Valenciennes, France
Lhoussain El Fadil Faculty of Sciences Dhar El Mahraz, P.O. Box 1796 Atlas-Fes, Sidi Mohamed ben Abdellah University, Morocco
Omar Kchit Graduate Normal School of Fez, Sidi Mohamed ben Abdellah University, Morocco
Bouchaïb Sodaïgui Université Polytechnique Hauts-de-France Ceramaths FR, CNRS 2037F-59313 Valenciennes, France

Abstract

For each prime number $p \in \{2,3,5\}$, we establish sufficient conditions for a sextic number field to have a prescribed $p$-adic valuation of its index, and we illustrate our results with explicit computational examples.