TY - JOUR AU - Xianhua Li AU - Tao Zhao PY - 2012/01/25 Y2 - 2024/03/29 TI - $S\Phi$-Supplemented subgroups of finite groups JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 64 IS - 1 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2558 AB - 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 group $G$ under the assumption that every subgroup of a Sylow $p$-subgroup of $G$ with given order is $S\Phi$-supplemented in $G$. Some results about formations are also obtained. ER -