Browse > Article
http://dx.doi.org/10.4134/JKMS.2013.50.3.579

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)
Publication Information
Journal of the Korean Mathematical Society / v.50, no.3, 2013 , pp. 579-589 More about this Journal
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
a normal subgroup; a self-normalizing subgroup; an NSN-group; a minimal non-NSN-group;
Citations & Related Records
연도 인용수 순위
  • Reference
1 R. Brandl, Groups with few non-normal subgroups, Comm. Algebra 23 (1995), no. 6, 2091-2098.   DOI   ScienceOn
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.   DOI
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.   DOI   ScienceOn
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.   DOI
11 G. L. Walls, Groups with maximal subgroups of Sylow subgroups normal, Israel J. Math. 43 (1982), no. 2, 166-168.   DOI
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).