论文标题
在有限的完全2封群体上
On finite totally 2-closed groups
论文作者
论文摘要
一个抽象的组$ g $被称为$ 2 $ cupted，如果$ h = h = h^{（2），ω} $，对于任何设置的$ω$，带有$ g \ g \ cong h \ leq {\ rm sym}（ω）$，其中$ h^{（2），ω}，ω} $是$ sems $ {$ rm rm {$ rm rm {相同的轨道为$ h $。在本文中，我们将有限的可溶性群体分类为2美元。我们还证明，完全$ 2 $的集团的合适子组是一个完全$ 2 $的集团。最后，我们证明，有限的不溶性完全$ 2 $ cluct的$ g $最低订单的最小订单，非平凡的配件子组具有$ z \ cdot x $，带有$ z = z（g）$ cyclic，$ x $是一个有限的组，具有一个独特的最小普通子系，是非平原的。
An abstract group $G$ is called totally $2$-closed if $H=H^{(2),Ω}$ for any set $Ω$ with $G\cong H\leq{\rm Sym}(Ω)$, where $H^{(2),Ω}$ is the largest subgroup of ${\rm Sym}(Ω)$ whose orbits on $Ω\timesΩ$ are the same orbits of $H$. In this paper, we classify the finite soluble totally $2$-closed groups. We also prove that the Fitting subgroup of a totally $2$-closed group is a totally $2$-closed group. Finally, we prove that a finite insoluble totally $2$-closed group $G$ of minimal order with non-trivial Fitting subgroup has shape $Z\cdot X$, with $Z=Z(G)$ cyclic, and $X$ is a finite group with a unique minimal normal subgroup, which is nonabelian.
