Bull. Korean Math. Soc. 2018; 55(6): 1835-1843
Online first article September 10, 2018 Printed November 30, 2018
https://doi.org/10.4134/BKMS.b171107
Copyright © The Korean Mathematical Society.
Pengfei Bai, Xiuyun Guo, Junxin Wang
Shanxi University of Finance and Economics, Shanghai University, Shanxi University of Finance and Economics
In this paper, finite $p$-groups $G$ satisfying $N_G(H)\leq H^G$ for every non-normal subgroup $H$ of $G$ are completely classified. This solves a problem proposed by Y. Berkovich.
Keywords: normalizer, normal closure, Dedekind $p$-group, $p$-group of maximal class
MSC numbers: 20D15, 20D25
2005; 42(3): 639-652
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