On minimal non-$\mathcal{QNS}$-groups
Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 1063-1073
https://doi.org/10.4134/BKMS.2014.51.4.1063
Published online July 31, 2014
Zhangjia Han, Huaguo Shi, and Guiyun Chen
Chengdu University of Information Technology, Sichuan Vocational and Technical College, Southwest University
Abstract : A finite group $G$ is called a $\mathcal{QNS}$-group if every minimal subgroup $X$of $G$ is either quasinormal in $G$ or self-normalizing. In this paper the authors classify the non-$\mathcal{QNS}$-groups whose proper subgroups are all $\mathcal{QNS}$-groups.
Keywords : minimal subgroups, quasinormal subgroups, self-normalizing subgroups, $\mathcal{QNS}$-groups, minimal non-$\mathcal{QNS}$-groups
MSC numbers : 20D35, 20E34
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