论文标题
关于确切的分区，$ 5 $的班级数量的一些纯Metacyclic字段数
On the exact divisibility by $5$ of the class number of some pure metacyclic fields
论文作者
论文摘要
令$γ\，= \，\ Mathbb {q}（\ sqrt [5] {n}）$是一个纯五重奏字段，其中$ n $是自然数量$ 5^{th} $无功能。令$ k = \ mathbb {q}（\ sqrt [5] {n}，ζ_5）$，使用$ζ_5$是单位的原始$ 5^{th} $，是$γ$的正常闭合，而纯度的Metacyclic Field和$ 20 $ $ 20 $ $ \ MATHBBBB的纯Metacyclic领域。当$ n $采用某些特定表格时，我们表明$γ$承认一个微不足道的$ 5 $级别的组，$ 5 $将$ k $的班级数完全划分。
Let $Γ\,=\, \mathbb{Q}(\sqrt[5]{n})$ be a pure quintic field, where $n$ is a natural number $5^{th}$ power-free. Let $k = \mathbb{Q}(\sqrt[5]{n}, ζ_5)$, with $ζ_5$ is a primitive $5^{th}$ root of unit, be the normal closure of $Γ$, and a pure metacyclic field of degree $20$ over $\mathbb{Q}$. When $n$ takes some particular forms, we show that $Γ$ admits a trivial $5$-class group and $5$ divides exactly the class number of $k$.
