论文标题
在给定的有限群体上
On finite groups with given $ICΦ$-subgroups
论文作者
论文摘要
如果$ h \ cap [h，g] \leφ（h）$，$ g $ $ g $的亚组$ h $被称为$ g $ $ g $。我们在假设某些给定的子组为$ g $的$icφ$ -subgroups $ g $的假设下分析了有限的$ g $。将获得有限的亚伯利亚团体和一些新标准的新特征，以$ 2 $ nilpotence和有限群体的niltectence的新标准。此外，我们将获得一个有限组的两个标准，以置于包含有限超溶剂类别类别的给定饱和形成中。
A subgroup $H$ of a group $G$ is said to be an $ICΦ$-subgroup of $G$ if $H \cap [H,G] \le Φ(H)$. We analyze the structure of a finite group $G$ under the assumption that some given subgroups of $G$ are $ICΦ$-subgroups of $G$. A new characterization of finite abelian groups and some new criteria for $2$-nilpotence and nilpotence of finite groups will be obtained. Moreover, we will obtain two criteria for a finite group to lie in a given solvably saturated formation containing the class of finite supersolvable groups.
