Finite groups which are minimal with respect to s-quasinormality and self-normality
Bull. Korean Math. Soc. 2013 Vol. 50, No. 6, 2079-2087
https://doi.org/10.4134/BKMS.2013.50.6.2079
Published online November 1, 2013
Zhangjia Han, Huaguo Shi, and Wei Zhou
Chengdu University of Information Technology, Sichuan Vocational and Technical College, Southwest University
Abstract : An $\mathcal{SQNS}$-group $G$ is a group in which every proper subgroup of $G$ is either s-quasinormal or self-normalizing and a minimal non-$\mathcal{SQNS}$-group is a group which is not an $\mathcal{SQNS}$-group but all of whose proper subgroups are $\mathcal{SQNS}$-groups. In this note all the finite minimal non-$\mathcal{SQNS}$-groups are determined.
Keywords : s-quasinormal subgroups, self-normalizing subgroups, $\mathcal{SQNS}$-groups, minimal non-$\mathcal{SQNS}$-groups
MSC numbers : 20D35, 20E34
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