论文标题
$ 5 $ - 类的发电机组的某些字段20度20 $ \ mathbb {q} $
The generators of $5$-class group of some fields of degree 20 over $\mathbb{Q}$
论文作者
论文摘要
令$γ\，= \，\ Mathbb {q}（\ sqrt [5] {n}）$为一个纯五重的字段，其中$ n $是一个正整数，$ 5^{th} $ power-power-power-power-fore。令$ k_0 \，= \，\ mathbb {q}（ζ_5）$为cyclotomic字段，其中包含一个原始的$ 5^{th} $ unity $ζ_5$和$ζ_5$和$ K \，= \，= \，γ（ζ_5）$的正常关闭是$ $γ$的正常关闭。令$ c_ {k，5} $为k类组的$ 5 $ - 组件。本文的目的是确定$ c_ {k，5} $的发电机，每当其类型为$（5,5）$，并且在$ gal（k/k_0）\，= \，\langleσ\ rangle $ as Cance中的歧义类别等级是$ 1 $。
Let $Γ\,=\, \mathbb{Q}(\sqrt[5]{n})$ be a pure quintic field, where $n$ is a positive integer, $5^{th}$ power-free. Let $k_0\,=\,\mathbb{Q}(ζ_5)$ be the cyclotomic field containing a primitive $5^{th}$ root of unity $ζ_5$, and $k\,=\,Γ(ζ_5)$ be the normal closure of $Γ$. Let $C_{k,5}$ be the $5$-component of the class group of k. The purpose of this paper is to determine generators of $C_{k,5}$, whenever it is of type $(5,5)$ and the rank of the group of ambiguous classes under the action of $Gal(k/k_0)\, =\,\langle σ\rangle$ is $1$.
