$\ell$-Class groups of fields in Kummer towers

Jianing Li, Yi Ouyang, Yue Xu +1

Let $\ell$ and $p$ be prime numbers and $K_{n,m}=\mathbb{Q}(p^{\frac{1}{{\ell }^n}},{\zeta }_{2{\ell }^m})$. We study the $\ell$-class group of $K_{n,m}$ in this paper. When $\ell =2$, we dete…