대한수학회지 (Journal of the Korean Mathematical Society)

  • 제46권6호
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  • Pages.1165-1178
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  • 2009
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
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FINITE GROUPS WHICH HAVE MANY NORMAL SUBGROUPS

  • Zhang, Qinhai (DEPARTMENT OF MATHEMATICS SHANXI NORMAL UNIVERSITY) ;
  • Guo, Xiaoqiang (DEPARTMENT OF MATHEMATICS HEBEI POLYTECHNIC UNIVERSITY) ;
  • Qu, Haipeng (DEPARTMENT OF MATHEMATICS SHANXI NORMAL UNIVERSITY) ;
  • Xu, Mingyao (DEPARTMENT OF MATHEMATICS SHANXI NORMAL UNIVERSITY)
  • 발행 : 2009.11.01
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초록

In this paper we classify finite groups whose nonnormal subgroups are of order p or pq, where p, q are primes. As a by-product, we also classify the finite groups in which all nonnormal subgroups are cyclic.

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참고문헌

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피인용 문헌

  1. The number of conjugacy classes of nonnormal subgroups of finite p -groups vol.466, 2016, https://doi.org/10.1016/j.jalgebra.2016.06.027
  2. FINITE NON-NILPOTENT GENERALIZATIONS OF HAMILTONIAN GROUPS vol.48, pp.6, 2011, https://doi.org/10.4134/BKMS.2011.48.6.1147
  3. Finite 2-groups whose nonnormal subgroups have orders at most 23 vol.7, pp.5, 2012, https://doi.org/10.1007/s11464-012-0216-3
  4. Generalised norms in finite soluble groups vol.402, 2014, https://doi.org/10.1016/j.jalgebra.2013.12.012
  5. Finite groups in which the normal closures of non-normal subgroups have the same order vol.15, pp.07, 2016, https://doi.org/10.1142/S0219498816501255
  6. On finite p-groups with few normal subgroups vol.16, pp.08, 2017, https://doi.org/10.1142/S0219498817501596
  7. Finite p-groups whose nonnormal subgroups have orders at most p 3 vol.9, pp.5, 2014, https://doi.org/10.1007/s11464-014-0389-z
  8. NOMALIZERS OF NONNORMAL SUBGROUPS OF FINITE p-GROUPS vol.49, pp.1, 2012, https://doi.org/10.4134/JKMS.2012.49.1.201
  9. Groups with Certain Normality Conditions vol.44, pp.8, 2016, https://doi.org/10.1080/00927872.2015.1044104
  10. Finite 2-groups whose length of chain of nonnormal subgroups is at most 2 vol.13, pp.5, 2018, https://doi.org/10.1007/s11464-018-0719-7
  11. Finite p-groups whose non-normal subgroups have few orders vol.13, pp.4, 2018, https://doi.org/10.1007/s11464-018-0693-0