Let $G$ be a finite group. A subgroup $H$ of $G$ is said to be weaklyS-embedded in $G$ if there exists $K\unlhd G$ such that $HK$ is S-quasinormalin $G$ and $H\cap K\leq H_{seG}$, where $H_{seG}$ is the subgroup generated byall those subgroups of $H$ which are S-quasinormally embedded in $G$. We saythat $H$ is weakly $\tau$-embedded in $G$ if there exists $K\unlhd G$ such that$HK$ is S-quasinormal in $G$ and $H\cap K\leq H_{\tau G}$, where $H_{\tau G}$is the subgroup generated by all those subgroups of $H$ which are$\tau$-quasinormal in $G$. In this paper, we study the properties of the weaklyS-embedded subgroups and the weakly $\tau$-embedded subgroups, and use them todetermine the structure of finite groups.
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机译：令$ G $为有限群。如果存在$ K \ unlhd G $，使得$ HK $是S-拟正态$ G $和$ H \ cap K \ leq H_，则据说$ G $的一个子组$ H $弱地嵌入在$ G $中。 {seG} $，其中$ H_ {seG} $是由所有$ H $子组生成的子组，这些子组准S一般嵌入在$ G $中。我们说，如果存在$ K \ unlhd G $，则$ H $弱地嵌入在$ G $中，使得$ HK $在$ G $和$ H \ cap K \ leq H _ {\ tau G} $，其中$ H _ {\ tau G} $是由所有$ H $子组生成的子组，这些子组在$ G $中是$ \ tau $-准正规的。在本文中，我们研究了弱S嵌入子群和弱$ \ tau $嵌入子群的性质，并用它们来确定有限群的结构。
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