论文标题
在具有透明因子亚组的分解组上
On factorized groups with permutable subgroups of factors
论文作者
论文摘要
一个组$ a $ a $ a $ a $和$ b $〜$ g $称为{\ rm msp} -permutable，如果以下语句保留：$ ab $〜是一个〜$ g $的子组；子组$ p $和$ q $是相互限制的，其中$ p $〜是任意的sylow $ p $ -subgroup〜$ a $ a $和$ q $〜是任意的sylow $ q $ q $ -subgroup〜$ b $，$ {p \ neq q} $。在本文中，我们研究了通过两个{\ rm MSP} - 可渗透子组分解的组。特别地，证明了两个supersoluble {\ rm MSP}的产物的超溶性证明了permutable子组。
The subgroups $A$ and $B$ of a group~$G$ are called {\rm msp}-permutable, if the following statements hold: $AB$~is a subgroup of~$G$; the subgroups $P$ and $Q$ are mutually permutable, where $P$~is an arbitrary Sylow $p$-subgroup of~$A$ and $Q$~is an arbitrary Sylow $q$-subgroup of~$B$, ${p\neq q}$. In the present paper, we investigate groups that factorized by two {\rm msp}-permutable subgroups. In particular, the supersolubility of the product of two supersoluble {\rm msp}-permutable subgroups is proved.
