Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

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.

Finite $p$-groups in which the normalizer of every non-normal subgroup is contained in its normal closure

Pengfei Bai, Xiuyun Guo, Junxin Wang

Shanxi University of Finance and Economics, Shanghai University, Shanxi University of Finance and Economics

Abstract

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