On common index divisors and monogenity of septic number fields defined by trinomials of type $x^7+ax^5+b$
Year: 2024
Type: article
Abstract: Let $K $ be a septic number field generated by a complex root $þ$ of a monic irreducible trinomial $ F(x)= x^7+ax^5+b \in \Z[x]$. Let $i(K)$ be the index of $K$. In this paper, we show that $i(K) \in \{1, 2, 4\}$. In a such way, we answer to Problem $22$ of Narkiewicz \cite{Na} for these number fields. In particular, we provide sufficient conditions for which $K$ is non-monogenic. We illustrate our results by some computational examples.
Source: Mathematica Bohemica
Author: Hamid Ben Yakkou
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404072403