The rank of the 2-class group of some fields with large degree

Abstract

Let $n\ge 3$ be an integer and $d$ an odd square-free integer. We shall compute the rank of the $2$-class group of $L_{n,d}:=\mathbb{Q}({\zeta }_{2^n},\sqrt{d})$, when all the prime divisors of $d$ are congruent to $\pm 3(\mathrm{mod}8)$ or $9(\mathrm{mod}16)$.

9 pages

References in corpus (2)

• $\ell$-Class groups of fields in Kummer towers
• On the $2$-class group of some number fields with large degree

Cited by in corpus (2)

• On the Hilbert $2$-class field towers of some cyclotomic ${\mathbb{Z}}_2$-extensions
• Hilbert genus fields of some number fields with high degrees