<i>Q</i> -permutable subgroups of finite groups

  • L. Miao School Math. Sci., Yangzhou Univ., China
  • Zh. Pu School Math. and Statistics, Hexi Univ., China


A subgroup $H$ of a group $G$ is called $Q$-permutable in $G$ if there exists a subgroup $B$ of $G$ such that (1) $G = HB$ and (2) if $H_1$ is a maximal subgroup of $H$ containing $H_{QG}$, then $H_1B = BH_1 < G$, where $H_{QG}$ is the largest permutable subgroup of $G$ contained in $H$. In this paper we prove that: Let $F$ be a saturated formation containing $U$ and $G$ be a group with a normal subgroup $H$ such that $G/H \in F$. If every maximal subgroup of every noncyclic Sylow subgroup of $F∗(H)$ having no supersolvable supplement in $G$ is $Q$-permutable in $G$, then $G \in F$.
How to Cite
Miao, L., and Z. Pu. “<i>Q</I&gt; -Permutable Subgroups of Finite Groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 11, Nov. 2011, pp. 1534-43, https://umj.imath.kiev.ua/index.php/umj/article/view/2823.
Research articles