有限群的弱S-拟正规嵌入子群

群G的子群H称为在G中S-拟正规嵌入的,如果对于任意的素数p||H|,H的Sylow p-子群也是G的某个S-拟正规子群的Sylow p-子群.称群G的子群H在G中弱S-拟正规嵌入,如果存在群G的正规子群T,使得HT■G且H∩T在G中是S-拟正规嵌入的.研究了弱S-拟正规嵌入子群的性质,给出了某些群类的新的特征,并推广了一些已知的结论.

Finite Groups with Weakly S-Quasinormally Embedded Subgroups

A subgroup $H$ of $G$ is called $S$-quasinormally embedded in $G$ if for each prime $p mid |H|$, a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $S$-quasinormal subgroup of $G$. A subgroup $H$ of $G$ is called weakly $S$-quasinormally embedded in $G$ if there exists a normal subgroup $T$ of $G$ such that $HT unlhd G$ and $H cap T$ is $S$-quasinormally embedded in $G$. The properties of weakly $S$-quasinormally embedded subgroups are obtained. The new characterizations of some classes of finite groups are given and some previously known results are generalized.