The generators of $5$-class group of some fields of degree 20 over $\mathbb{Q}$

Fouad Elmouhib, Mohamed Talbi, Abdelmalek Azizi

Let $\Gamma =\mathbb{Q}(\sqrt[5]{n})$ be a pure quintic field, where $n$ is a positive integer, $5^{th}$ power-free. Let $k_0=\mathbb{Q}({\zeta }_5)$ be the cyclotomic field containing…