# The nc-supplemented subgroups of finite groups

Document Type : Research Paper

Authors

1 School of Science, Sichuan University of Science & Engineering, 643000, Zigong, P. R. China

2 School of Mathematics and Statistics, Chongqing University of Arts and Sciences, 402160, Chongqing, P. R. China

Abstract

A subgroup $H$ is said to be
$nc$-supplemented in a group $G$ if there exists a subgroup $Kleq G$
such that $HKlhd G$ and $Hcap K$ is contained in $H_{G}$, the core
of $H$ in $G$. We characterize the supersolubility of finite groups $G$
with that every maximal subgroup of the Sylow subgroups is $nc$-supplemented in $G$.

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Main Subjects

### History

• Receive Date: 10 September 2011
• Revise Date: 24 September 2012
• Accept Date: 24 November 2012
• First Publish Date: 15 December 2013