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Bull. Korean Math. Soc. 2014; 51(4): 1135-1144

Printed July 31, 2014

https://doi.org/10.4134/BKMS.2014.51.4.1135

Copyright © The Korean Mathematical Society.

Finite groups all of whose maximal subgroups are SB-groups

Pengfei Guo, Junxin Wang, and Hailiang Zhang

City University of Hong Kong, Shanxi University of Finance and Economics, Zhejiang Ocean University

Abstract

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A finite group $G$ is called a SB-group if every subgroup of $G$ is either $s$-quasinormal or abnormal in $G$. In this paper, we give a complete classification of those groups which are not SB-groups but all of whose proper subgroups are SB-groups.

Keywords: SB-group, minimal non-SB-group, supersolvable group, power automorphism

MSC numbers: Primary 20D10, 20E34

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