$A generalization of $c$-Supplementation$

A generalization of $c$-Supplementation

A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there is a subgroup $K\leq G$ such that $HK\unlhd G$ and $H\cap K$ is contained in $H_G$, the core of $H$ in $G$. We characterize the solvability of finite groups $G$ with some subgroups of Sylow subgroups $nc$-su...

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Veröffentlicht in:	arXiv.org 2005-09
Hauptverfasser:	Li, Shiheng, Liang, Dengfeng, Shi, Wujie
Format:	Artikel
Sprache:	eng
Schlagworte:	Subgroups
Online-Zugang:	Volltext
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Zusammenfassung:	A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there is a subgroup $K\leq G$ such that $HK\unlhd G$ and $H\cap K$ is contained in $H_G$, the core of $H$ in $G$. We characterize the solvability of finite groups $G$ with some subgroups of Sylow subgroups $nc$-supplemented in $G$. We also give a result on $c$-supplemented subgroups.
ISSN:	2331-8422

Zusammenfassung:	A subgroup \(H\) is said to be \(nc\)-supplemented in a group \(G\) if there is a subgroup \(K\leq G\) such that \(HK\unlhd G\) and \(H\cap K\) is contained in \(H_G\), the core of \(H\) in \(G\). We characterize the solvability of finite groups \(G\) with some subgroups of Sylow subgroups \(nc\)-supplemented in \(G\). We also give a result on \(c\)-supplemented subgroups.
ISSN:	2331-8422

A generalization of \(c\)-Supplementation