On index divisors and monogenity of certain sextic number fields defined by $x^6+ax^5+b$

Lhoussain El Fadil; Omar Kchit

On index divisors and monogenity of certain sextic number fields defined by $x^6+ax^5+b$

Number Theory 2022-07-19 v1

Authors: Lhoussain El Fadil , Omar Kchit

Abstract

The main goal of this paper is to provide a complete answer to the Problem 22 of Narkiewicz \cite{Nar} for any sextic number field $K$ generated by a complex root $\alpha$ of a monic irreducible trinomial $F(x) = x^6+ax^5+b \in \mathbb{Z}[x]$ . Namely we calculate the index of the field $K$ . In particular, if $i(K)\neq 1$ , then $K$ is not mongenic. Finally, we illustrate our results by some computational examples.

Keywords

sextic number field index divisor monogenity trinomial algebraic number theory

Cite

@article{arxiv.2206.05529,
  title  = {On index divisors and monogenity of certain sextic number fields defined by $x^6+ax^5+b$},
  author = {Lhoussain El Fadil and Omar Kchit},
  journal= {arXiv preprint arXiv:2206.05529},
  year   = {2022}
}

Comments

submitted. arXiv admin note: text overlap with arXiv:2204.03226

On index divisors and monogenity of certain sextic number fields defined by $x^6+ax^5+b$

Abstract

Keywords

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