• Zhang, Qinhai ;
  • Gao, Juan
  • Received : 2010.10.21
  • Published : 2012.01.01


Assume G is a finite p-group and i is a fixed positive integer. In this paper, finite p-groups G with ${\mid}N_G(H):H{\mid}=p^i$ for all nonnormal subgroups H are classified up to isomorphism. As a corollary, this answer Problem 116(i) proposed by Y. Berkovich in his book "Groups of Prime Power Order Vol. I" in 2008.


finite p-groups;nonnormal subgroups;self-normalizer;central extensions


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Supported by : NSFC, NSF of Shanxi Province