Finite Groups with Weakly $s$-Permutably Embedded and Weakly $s$-Supplemented Subgroups

Changwen Li¹

¹ School of Mathematical Science Xuzhou Normal University Xuzhou, 221116, China

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 1, pp. 41-52

Résumé

Suppose $G$ is a finite group and $H$ is a subgroup of $G$. $H$ is called weakly $s$-permutably embedded in $G$ if there are a subnormal subgroup $T$ of $G$ and an $s$-permutably embedded subgroup $H_{se}$ of $G$ contained in $H$ such that $G=HT$ and $H\cap T\leq H_{se}$; $H$ is called weakly $s$-supplemented in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $H\cap T\leq H_{sG}$, where $H_{sG}$ is the subgroup of $H$ generated by all those subgroups of $H$ which are $s$-permutable in $G$. We investigate the influence of the existence of $s$-permutably embedded and weakly $s$-supplemented subgroups on the structure of finite groups. Some recent results are generalized.

Détail

DOI : 10.4064/ba59-1-6

Keywords: suppose finite group subgroup called weakly s permutably embedded there subnormal subgroup s permutably embedded subgroup contained cap leq called weakly s supplemented there subgroup cap leq where subgroup generated those subgroups which s permutable investigate influence existence s permutably embedded weakly s supplemented subgroups structure finite groups recent results generalized