论文标题
有限的注释完全$ 2 $ clup的置换组
Notes on finite totally $2$-closed permutation groups
论文作者
论文摘要
令$ n $为有限组$ g $的普通亚组。对于忠实的$ n $ set $δ$，应用嵌入定理的大学可以构建一个忠实的$ g $ -set $ω$。在此简短说明中，可以证明，如果$ n $ $ n $ in $ω$等于$ n $，则$ n $ $ n $ in $δ$也等于$ n $;此外，事实证明，所有有限的Abelian普通亚组完全$ 2 $ clucted的组都是循环的。最后，事实证明，如果有限的nilpotent群体是两个尼尔氏型亚组的直接，这两个因素具有codrime订单，并且两个因素都完全2关，那么g完全$ 2 $ 2 $。作为推论，以更简单的方式重复了有限的完全2封闭组的几个众所周知的结果。
Let $N$ be a normal subgroup of a finite group $G$. For a faithful $N$-set $Δ$, applying the university embedding theorem one can construct a faithful $G$-set $Ω$. In this short note, it is proved that if the $2$-closure of $N$ in $Ω$ is equal to $N$, then the $2$-closure of $N$ in $Δ$ is also equal to $N$; in addition, it is proved that any abelian normal subgroup of a finite totally $2$-closed group is cyclic; finally, it is proved that if a finite nilpotent group is a direct of two nilpotent subgroups where the two factors have coprime orders and both of them are totally 2-closed then G is totally $2$-closed. As corollaries, several well-known results on finite totally 2-closed groups are reproved in more simple ways.
