1. The influence of weakly-supplemented subgroups on the structure of finite groups
- Creator:
- Kong, Qingjun and Liu, Qingfeng
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- weakly-supplemented subgroup, $p$-nilpotent group, and supersolvable group
- Language:
- English
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public