JOURNAL BROWSE
Search
Advanced SearchSearch Tips
FINITE GROUPS ALL OF WHOSE MAXIMAL SUBGROUPS ARE SB-GROUPS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
FINITE GROUPS ALL OF WHOSE MAXIMAL SUBGROUPS ARE SB-GROUPS
Guo, Pengfei; Wang, Junxin; Zhang, Hailiang;
  PDF(new window)
 Abstract
A finite group G is called a SB-group if every subgroup of G is either s-quasinormal or abnormal in G. In this paper, we give a complete classification of those groups which are not SB-groups but all of whose proper subgroups are SB-groups.
 Keywords
SB-group;minimal non-SB-group;supersolvable group;power automorphism;
 Language
English
 Cited by
 References
1.
R. K. Agrawal, Finite groups whose subnormal subgroups permute with all Sylow subgroups, Proc. Amer. Math. Soc. 47 (1975), no. 1, 77-83. crossref(new window)

2.
A. Ballester-Bolinches and R. Esteban-Romero, On minimal non-supersoluble groups, Rev. Mat. Iberoamericana 23 (2007), no. 1, 127-142.

3.
A. Ballester-Bolinches, R. Esteban-Romero, and D. J. S. Robinson, On finite minimal non-nilpotent groups, Proc. Amer. Math. Soc. 133 (2005), no. 12, 3455-3462. crossref(new window)

4.
K. Doerk, Minimal nicht uberauflosbare, endliche Gruppen, Math. Z. 91 (1966), 198-205. crossref(new window)

5.
A. Fattahi, Groups with only normal and abnormal subgroups, J. Algebra 28 (1974), 15-19. crossref(new window)

6.
P. F. Guo and X. Y. Guo, On minimal non-MSN-groups, Front. Math. China 6 (2011), no. 5, 847-854. crossref(new window)

7.
X. Y. Guo, K. P. Shum, and A. Ballester-Bolinches, On complemented minimal subgroups in finite groups, J. Group Theory 6 (2003), no. 2, 159-167.

8.
Z. J. Han, G. Y. Chen, and W. Zhou, On minimal non-NSN-groups, J. Korean Math. Soc. 50 (2013), no. 3, 579-589. crossref(new window)

9.
S. R. Li, On minimal non-PE-groups, J. Pure Appl. Algebra 132 (1998), no. 2, 149-158. crossref(new window)

10.
D. J. S. Robinson, A Course in the Theory of Groups, Springer-Verlag, New York-Heidelberg-Berlin, 1982.

11.
D. J. S. Robinson, Minimality and Sylow-permutability in locally finite groups, Ukrainian Math. J. 54 (2002), no. 6, 1038-1048. crossref(new window)

12.
O. J. Schmidt, Uber Gruppen, deren samtliche Teiler spezielle Gruppen sind, Mat. Sbornik 31 (1924), 366-372.

13.
Z. C. Shen, S. R. Li, and W. J. Shi, Finite groups all of whose second maximal subgroups are PSC-groups, J. Algebra Appl. 8 (2009), no. 2, 229-242. crossref(new window)

14.
J. G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc. 74 (1968), 383-437. crossref(new window)

15.
M. Y. Xu and Q. H. Zhang, On conjugate-permutable subgroups of a finite group, Algebra Colloq. 12 (2005), no. 4, 669-676. crossref(new window)

16.
Q. H. Zhang, Finite groups with only s-quasinormal and abnormal subgroups, Northeast. Math. J. 14 (1998), no. 1, 41-46.

17.
Q. H. Zhang, s-semipermutability and abnormality in finite groups, Comm. Algebra 27 (1999), no. 9, 4515-4524. crossref(new window)

18.
Y. Zhao, A note on the structure of Quasi-Hamilton groups, J. Engineering Math. 9 (1992), no. 4, 119-121.