$S\Phi$-Supplemented subgroups of finite groups

• Date: 2012
• Main Authors: Li, Xianhua, Zhao, Tao, Лі, Хіаньхуа, Чжао, Тао
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2558
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We call $H$ an $S\Phi$-supplemented subgroup of a finite group $G$ if there exists a subnormal subgroup $T$ of $G$ such that $G = HT$ and $H \bigcap T \leq \Phi(H)$, where $\Phi(Н)$ is the Frattini subgroup of $H$. In this paper, we characterize the $p$-nilpotency and supersolubility of a finite g...