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arXiv · 1804.00692

The generators of $3$-class group of some fields of degree $6$ over $\mathbb{Q}$

Siham Aouissi·Moulay Chrif Ismaili·Mohamed Talbi·Abdelmalek Azizi
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Abstract

Let $\mathrm{k}=\mathbb{Q}\left(\sqrt[3]{p},\zeta_3\right)$, where $p$ is a prime number such that $p \equiv 1 \pmod 9$, and let $C_{\mathrm{k},3}$ be the $3$-component of the class group of $\mathrm{k}$. In \cite{GERTH3}, Frank Gerth III proves a conjecture made by Calegari and Emerton \cite{Cal-Emer} which gives necessary and sufficient conditions for $C_{\mathrm{k},3}$ to be of $\operatorname{rank}\,$ two. The purpose of the present work is to determine generators of $C_{\mathrm{k},3}$, whenever it is isomorphic to $\mathbb{Z}/9\mathbb{Z} \times \mathbb{Z}/3\mathbb{Z}$.

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Siham Aouissi, Moulay Chrif Ismaili, Mohamed Talbi, Abdelmalek Azizi. 2018-04-02. The generators of $3$-class group of some fields of degree $6$ over $\mathbb{Q}$. https://doi.org/10.5269/bspm.40672

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