The nc-supplemented subgroups of finite groups

Guo, S.; Liu, S.; Shi, W. J.

The nc-supplemented subgroups of finite groups

Document Type : Research Paper

Authors

S. Guo ¹
S. Liu ¹
W. J. Shi ²

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 $G$.

Keywords