论文标题
单位规范指数和$ p $ class组在某些程度上$ \ ell $扩展
The unit norm index and $p$-class group in certain degree $\ell$ extensions
论文作者
论文摘要
在某些条件下，我们检查了何时在域中的单位是扩展字段中元素的规范。我们将这些结果应用于反环体$ \ Mathbb {Z} _2 $ extension $ \ Mathbb {q}（i）$的$ \ ell $ class组的研究。
We examine when units in a field are the norms of elements in an extension field, given certain conditions. We apply these results to the study of the $\ell$-class groups in lifts of the anti-cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q}(i)$.
