$S\Phi$-Supplemented subgroups of finite groups

  • Xianhua Li School Math. Sci., Soochow Univ., Suzhou, China
  • Tao Zhao School Sci., Shandong Univ. Technology, Zibo, China)

Abstract

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.
Published
25.01.2012
How to Cite
LiX., and ZhaoT. “$S\Phi$-Supplemented Subgroups of Finite Groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 1, Jan. 2012, pp. 92-99, http://umj.imath.kiev.ua/index.php/umj/article/view/2558.
Section
Research articles