1. On $S$-quasinormal and $c$-normal subgroups of a finite group
- Creator:
- Li, Shirong and Li, Yangming
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- $S$-quasinormally embedded subgroup, $c$-normal subgroup, $p$-nilpotent group, the generalized Fitting subgroup;, and saturated formation
- Language:
- English
- Description:
- Let $\cal F$ be a saturated formation containing the class of supersolvable groups and let $G$ be a finite group. The following theorems are presented: (1) $G\in \cal F$ if and only if there is a normal subgroup $H$ such that $G/H\in \cal F$ and every maximal subgroup of all Sylow subgroups of $H$ is either $c$-normal or $S$-quasinormally embedded in $G$. (2) $G\in \cal F$ if and only if there is a normal subgroup $H$ such that $G/H\in \cal F$ and every maximal subgroup of all Sylow subgroups of $F^*(H)$, the generalized Fitting subgroup of $H$, is either $c$-normal or $S$-quasinormally embedded in $G$. (3) $G\in \cal F$ if and only if there is a normal subgroup $H$ such that $G/H\in \cal F$ and every cyclic subgroup of $F^*(H)$ of prime order or order 4 is either $c$-normal or $S$-quasinormally embedded in $G$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public