Siham Aouissi, Mohamed Talbi, Moulay Chrif Ismaili, Abdelmalek Azizi

On a Conjecture of Lemmermeyer

Let $p\equiv 1\,(\mathrm{mod}\,3)$ be a prime and denote by $\zeta_3$ a primitive third root of unity. Recently, Lemmermeyer presented a conjecture about $3$-class groups of pure cubic fields $L=\mathbb{Q}(\sqrt[3]{p})$ and of their normal closures $\mathrm{k}=\mathbb{Q}(\sqrt[3]{p},\zeta_3)$. The purpose of this paper is to prove Lemmermeyer’s conjecture.

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