Finite $p$-nilpotent groups with some subgroups weakly $ℳ$-supplemented

Dong, Liushuan. "Finite $p$-nilpotent groups with some subgroups weakly $\mathcal {M}$-supplemented." Czechoslovak Mathematical Journal 70.1 (2020): 291-297. <http://eudml.org/doc/297235>.

@article{Dong2020,
abstract = {Suppose that $G$ is a finite group and $H$ is a subgroup of $G$. Subgroup $H$ is said to be weakly $\mathcal \{M\}$-supplemented in $G$ if there exists a subgroup $B$ of $G$ such that (1) $G=HB$, and (2) if $H_\{1\}/H_\{G\}$ is a maximal subgroup of $H/H_\{G\}$, then $H_\{1\}B=BH_\{1\}<G$, where $H_\{G\}$ is the largest normal subgroup of $G$ contained in $H$. We fix in every noncyclic Sylow subgroup $P$ of $G$ a subgroup $D$ satisfying $1<|D|<|P|$ and study the $p$-nilpotency of $G$ under the assumption that every subgroup $H$ of $P$ with $|H|=|D|$ is weakly $\mathcal \{M\}$-supplemented in $G$. Some recent results are generalized.},
author = {Dong, Liushuan},
journal = {Czechoslovak Mathematical Journal},
keywords = {$p$-nilpotent group; weakly $\mathcal \{M\}$-supplemented subgroup; finite group},
language = {eng},
number = {1},
pages = {291-297},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite $p$-nilpotent groups with some subgroups weakly $\mathcal \{M\}$-supplemented},
url = {http://eudml.org/doc/297235},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Dong, Liushuan
TI - Finite $p$-nilpotent groups with some subgroups weakly $\mathcal {M}$-supplemented
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 1
SP - 291
EP - 297
AB - Suppose that $G$ is a finite group and $H$ is a subgroup of $G$. Subgroup $H$ is said to be weakly $\mathcal {M}$-supplemented in $G$ if there exists a subgroup $B$ of $G$ such that (1) $G=HB$, and (2) if $H_{1}/H_{G}$ is a maximal subgroup of $H/H_{G}$, then $H_{1}B=BH_{1}<G$, where $H_{G}$ is the largest normal subgroup of $G$ contained in $H$. We fix in every noncyclic Sylow subgroup $P$ of $G$ a subgroup $D$ satisfying $1<|D|<|P|$ and study the $p$-nilpotency of $G$ under the assumption that every subgroup $H$ of $P$ with $|H|=|D|$ is weakly $\mathcal {M}$-supplemented in $G$. Some recent results are generalized.
LA - eng
KW - $p$-nilpotent group; weakly $\mathcal {M}$-supplemented subgroup; finite group
UR - http://eudml.org/doc/297235
ER -