대한수학회지 (Journal of the Korean Mathematical Society)

  • 제49권1호
  • /
  • Pages.201-221
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  • 2012
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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NOMALIZERS OF NONNORMAL SUBGROUPS OF FINITE p-GROUPS

  • Zhang, Qinhai (Department of Mathematics Shanxi Normal University) ;
  • Gao, Juan (Department of Mathematics Shanxi Normal University)
  • 투고 : 2010.10.21
  • 발행 : 2012.01.01
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초록

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.

키워드

참고문헌

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피인용 문헌

  1. Some restrictions on normalizers or centralizers in finite p-groups vol.208, pp.1, 2015, https://doi.org/10.1007/s11856-015-1197-1
  2. Some finiteness conditions on normalizers or centralizers in groups 2018, https://doi.org/10.1080/00927872.2017.1363223
  3. Finite $$p$$ p -Groups all of Whose Nonnormal Subgroups Posses Special Normalizers vol.40, pp.1, 2017, https://doi.org/10.1007/s40840-016-0322-6
  4. A finiteness condition on centralizers in locally nilpotent groups vol.182, pp.2, 2017, https://doi.org/10.1007/s00605-015-0854-0