On Index Divisors and Monogenity of Certain Sextic Number Fields Defined by x6+ax5+b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^6+ax^5+b$$\end{document}Index Divisors and Monogenity of Certain Sextic Number FieldsL. El Fadil, O. Kchit

The main goal of this paper is to provide a complete answer to the Problem 22 of Narkiewicz (2004) for any sextic number field K generated by a root of a monic irreducible trinomial F(x)=x6+ax5+b∈Z[x]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F(x)=x^6+ax^5+b\in \mathbb {Z}[x]$$\end{document}. Namely, we calculate the index of the field K. In particular, if i(K)≠1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i(K)\ne 1$$\end{document}, then K is not mongenic. Finally, we illustrate our results by some computational examples.