Let $G$ be a finite group and $H$ a subgroup of $G$. $H$ is said to be $NH$-embedded in $G$ if there exists a normal subgroup $T$ of $G$ such that $HT$ is a Hall subgroup of $G$ and $H\cap T\le H_{\bar{s}G}$, where $H_{\bar{s}G}$ is the largest $s$-semipermutable subgroup of $G$ contained in $H$. In this paper, we give some new characterizations of $p$-nilpotent and supersolvable groups by using $NH$-embedded subgroups. Some known results are generalized.

中文翻译：

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关于有限群的 NH 嵌入子群

让$G$是一个有限群并且$H$一个子群$G$.$H$据说是$ñH$-嵌入$G$如果存在正规子群$吨$的$G$这样$H吨$是霍尔子群$G$和$H\cap 吨\le H_{\bar{s}G}$， 在哪里$H_{\bar{s}G}$是最大的$s$- 半可变子群$G$包含在$H$. 在本文中，我们给出了一些新的特征$p$-幂零和超可解组通过使用$ñH$- 嵌入式子组。一些已知的结果被概括了。