Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON MINIMAL NON-NSN-GROUPS

  • Han, Zhangjia (School of Mathematics Chengdu University of Information Technology) ;
  • Chen, Guiyun (School of Mathematics and Statistics Southwest University) ;
  • Shi, Huaguo (Sichuan Vocational and Technical College)
  • Received : 2012.07.29
  • Published : 2013.05.01
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Abstract

A finite group G is called an NSN-group if every proper subgroup of G is either normal in G or self-normalizing. In this paper, the non-NSN-groups whose proper subgroups are all NSN-groups are determined.

Keywords

References

  1. R. Brandl, Groups with few non-normal subgroups, Comm. Algebra 23 (1995), no. 6, 2091-2098. https://doi.org/10.1080/00927879508825330
  2. J. Buckley, J. C. Lennox, and J. Wieglod, Generalizations of Hamiltonian groups, Ricerche Mat. 41 (1992), no. 2, 369-376.
  3. S. Chen, Classification of finite groups whose maximal subgroups are Dedekind groups, J. Zhejiang Univ. Sci. Ed. 29 (2002), no. 2, 121-124.
  4. K. Doerk, Minimal nicht uberauflosbare endliche Gruppen, Math. Z. 91 (1966), 198-205. https://doi.org/10.1007/BF01312426
  5. H. Kurzweil and B. Stellmacher, The Theory of Finite Groups, An Introduction, New York: Springer-Verlag, 2004.
  6. T. J. Laffey, A lemma on finite p-group and some consequences, Proc. Cambr. Phil. Soc. 75 (1974), 133-137.
  7. G. A. Miller and H. C. Moreno, Non-abelian groups in which every subgroup is abelian, Trans. Amer. Math. Soc. 4 (1903), no. 4, 398-404. https://doi.org/10.1090/S0002-9947-1903-1500650-9
  8. Gh. Pic, On the structure of quasi-Hamiltonian groups, Acad. Repub. Pop. Romane Bul. Sti. A. 1 (1949), 973-979.
  9. D. J. S. Robinson, A Course in the Theory of Groups, New York, Springer, 1993.
  10. J. G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc. 74 (1968), 383-437. https://doi.org/10.1090/S0002-9904-1968-11953-6
  11. G. L. Walls, Groups with maximal subgroups of Sylow subgroups normal, Israel J. Math. 43 (1982), no. 2, 166-168. https://doi.org/10.1007/BF02761728
  12. Q. Zhang, Groups with only normal and self-normalzing subgroups, J. Shanxi Normal University (Science Edition) 3 (1989), no. 2, 11-13(in Chinese).

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