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arXiv · 2112.01133

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

Lhoussain El Fadil
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Abstract

The goal of this paper is to calculate explicitly the field index of any quintic number field $K$ generated by a complex root $\al$ of a monic irreducible trinomial $F(x) = x^5+ax+b \in \Z[x]$. In such a way we provide a complete answer to the Problem 22 of Narkiewicz \cite{WN}. Namely for every prime integer $p$, we evaluate the highest power of $p$ dividing $i(K)$. In particular, we give sufficient conditions on $a$ and $b$, which guarantee the non monogenity of $K$.

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Lhoussain El Fadil. 2021-12-02. On common index divisors and monogenity of certain number fields defined by $x^5+ax+b$. https://arxiv.org/abs/2112.01133

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