The influence of weakly-supplemented subgroups on the structure of finite groups

Title:

The influence of weakly-supplemented subgroups on the structure of finite groups

Creator:

Kong, Qingjun and Liu, Qingfeng

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:16fd189d-efbb-4ffe-b5ef-279a301df7a5
uuid:16fd189d-efbb-4ffe-b5ef-279a301df7a5

Subject:

weakly-supplemented subgroup, $p$-nilpotent group, and supersolvable group

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

A subgroup $H$ of a finite group $G$ is weakly-supplemented in $G$ if there exists a proper subgroup $K$ of $G$ such that $G=HK$. In the paper it is proved that a finite group $G$ is $p$-nilpotent provided $p$ is the smallest prime number dividing the order of $G$ and every minimal subgroup of $P\cap G'$ is weakly-supplemented in $N_{G}(P),$ where $P$ is a Sylow $p$-subgroup of $G$. As applications, some interesting results with weakly-supplemented minimal subgroups of $P\cap G'$ are obtained.

Language:

English

Rights:

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

Coverage:

173-182

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:1

Harvested from:

CDK

Metadata only:

false