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

Kong, Qingjun, and Liu, Qingfeng. "The influence of weakly-supplemented subgroups on the structure of finite groups." Czechoslovak Mathematical Journal 64.1 (2014): 173-182. <http://eudml.org/doc/262052>.

@article{Kong2014,
abstract = {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 $P\cap G^\{\prime \}$ 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 $P\cap G^\{\prime \}$ are obtained.},
author = {Kong, Qingjun, Liu, Qingfeng},
journal = {Czechoslovak Mathematical Journal},
keywords = {weakly-supplemented subgroup; $p$-nilpotent group; supersolvable group; finite groups; subgroup embedding properties; weakly supplemented subgroups; -nilpotent groups; supersolvable groups; Sylow subgroups; Sylow towers; formations},
language = {eng},
number = {1},
pages = {173-182},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The influence of weakly-supplemented subgroups on the structure of finite groups},
url = {http://eudml.org/doc/262052},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Kong, Qingjun
AU - Liu, Qingfeng
TI - The influence of weakly-supplemented subgroups on the structure of finite groups
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 173
EP - 182
AB - 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 $P\cap G^{\prime }$ 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 $P\cap G^{\prime }$ are obtained.
LA - eng
KW - weakly-supplemented subgroup; $p$-nilpotent group; supersolvable group; finite groups; subgroup embedding properties; weakly supplemented subgroups; -nilpotent groups; supersolvable groups; Sylow subgroups; Sylow towers; formations
UR - http://eudml.org/doc/262052
ER -