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FINITE p-GROUPS IN WHICH THE NORMALIZER OF EVERY NON-NORMAL SUBGROUP IS CONTAINED IN ITS NORMAL CLOSURE

  • Bai, Pengfei (School of Applied Mathematics Shanxi University of Finance and Economics) ;
  • Guo, Xiuyun (Department of Mathematics Shanghai University) ;
  • Wang, Junxin (School of Applied Mathematics Shanxi University of Finance and Economics)
  • Received : 2017.12.22
  • Accepted : 2018.08.02
  • Published : 2018.11.30

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.

Acknowledgement

Supported by : National Natural Science Foundation of China

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