论文标题
在一些可实现的Metabelian $ 5 $ -Groups
On some realizable metabelian $5$-groups
论文作者
论文摘要
令$ g $为$ 5 $ - 最大级别，$γ_2（g）= [g，g] $派生的组。假设Abelianization $ g/γ_2（g）$是类型$（5，5）$，而转移$ v_ {h_1 \toγ_2（g）} $和$ v_ {h_2 \toγ_2（g）$是$ h_1 $ and $ h_1 $ and $ h_2 $ sum y s tw t tw ymaxim sum $ g g，然后，$ g $由同构阶级组完全确定。此外，对于某些字段$ k $，该组$ g $是可以实现的，这是纯Quintic领域的正常关闭。
Let $G$ be a $5$-group of maximal class and $γ_2(G) = [G, G]$ its derived group. Assume that the abelianization $G/γ_2(G)$ is of type $(5, 5)$ and the transfers $V_{H_1\to γ_2(G)}$ and $V_{H_2\to γ_2(G)}$ are trivial, where $H_1$ and $H_2$ are two maximal normal subgroups of $G$. Then $G$ is completely determined with the isomorphism class groups of maximal class. Moreover the group $G$ is realizable with some fields $k$, which is the normal closure of a pure quintic field.
