INFINITE FAMILIES OF SEXTIC NUMBER FIELDS WITH ALL POSSIBLE INDICES

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

doi:10.5269/bspm.81060

INFINITE FAMILIES OF SEXTIC NUMBER FIELDS WITH ALL POSSIBLE 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 rational prime $p\in\{2,3,5\}$, we construct infinite families of sextic number fields $K$ such that the $p$-adic valuation of the index $i(K)$ satisfies $\nu_p(i(K))=\nu_p$, for every possible positive integer $\nu_p$. We illustrate our results by some computational examples.