论文标题
$ \ ell $ torsion in Class组II：nilpotent扩展
Pointwise Bound for $\ell$-torsion in Class Groups II: Nilpotent Extensions
论文作者
论文摘要
对于每个有限的$ p $ -group $ g_p $，是非环境和非Qualtnion的，以及每个大于$ 2 $的正整数$ \ ell \ neq p $，我们证明，在每个$ g_p $ -extension的分类组中，对$ \ ell $ torsion的第一个非平地限制。更一般而言，对于每个nilpotent $ g $，每个sylow- $ p $ subgroup $ g_p \ g_p \ subset g $都是非循环且非quatqualnion，我们证明，每一个$ g $ - exteension of g $ g $ etteger $ \ ell $ \ ell $ \ ell $ \ ell $ \ ell f eell> ell> 1 $ 1 $ 1 $ 1 $ 1 $。
For every finite $p$-group $G_p$ that is non-cyclic and non-quaternion and every positive integer $\ell\neq p$ 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 $\ell>1$.
