Pointwise Bound for $\ell$-torsion in Class Groups II: Nilpotent Extensions

Abstract

For every finite $p$-group $G_p$ that is non-cyclic and non-quaternion and every positive integer $\ell \ne p$ that is greater than $2$, we prove the first non-trivial bound on $\ell$-torsion in class group of every $G_p$-extension. More generally, for every nilpotent group $G$ where every Sylow-$p$ subgroup $G_p\subset G$ is non-cyclic and non-quaternion, we prove a non-trivial bound on $\ell$-torsion in class group of every $G$-extension for every integer $\ell >1$.

References in corpus (1)

• Bounds for the $\ell$-torsion in class groups