$3$-Principalization over $S_3$-fields

Siham Aouissi, Mohamed Talbi, Daniel C. Mayer +1

Let $p\equiv 1(\mathrm{mod}9)$ be a prime number and ${\zeta }_3$ be a primitive cube root of unity. Then $\mathrm{k}=\mathbb{Q}(\sqrt[3]{p},{\zeta }_3)$ is a pure metacyclic field with grou…