Finite $p$-groups in which the normalizer of every non-normal subgroup is contained in its normal closure
Bull. Korean Math. Soc. 2018 Vol. 55, No. 6, 1835-1843
Published online September 10, 2018
Printed November 30, 2018
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
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