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 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 https://doi.org/10.4134/BKMS.b171107Published online 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 Downloads: Full-text PDF