On $S$-quasinormal and $c$-normal subgroups of a finite group

Title:

On $S$-quasinormal and $c$-normal subgroups of a finite group

Creator:

Li, Shirong and Li, Yangming

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:eb637524-2d0e-4528-a693-0a426a4894a6
uuid:eb637524-2d0e-4528-a693-0a426a4894a6

Subject:

$S$-quasinormally embedded subgroup, $c$-normal subgroup, $p$-nilpotent group, the generalized Fitting subgroup;, and saturated formation

Type:

model:article and TEXT

Format:

bez média and svazek

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 $G$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1083-1095

Source:

Czechoslovak Mathematical Journal | 2008 Volume:58 | Number:4

Harvested from:

CDK

Metadata only:

false