On minimal non-MSN-groups

Pengfei Guo , Xiuyun Guo

Front. Math. China ›› 2011, Vol. 6 ›› Issue (5) : 847 -854.

PDF (96KB)
Front. Math. China ›› 2011, Vol. 6 ›› Issue (5) : 847 -854. DOI: 10.1007/s11464-011-0115-z
Research Article
RESEARCH ARTICLE

On minimal non-MSN-groups

Author information +
History +
PDF (96KB)

Abstract

A finite group G is called an MSN-group if all maximal subgroups of the Sylow subgroups of G are subnormal in G. In this paper, we determinate the structure of non-MSN-groups in which all of whose proper subgroups are MSN-groups.

Keywords

Subnormal group / maximal subgroup / MSN-group / minimal non-MSN-group / automorphism

Cite this article

Download citation ▾
Pengfei Guo, Xiuyun Guo. On minimal non-MSN-groups. Front. Math. China, 2011, 6(5): 847-854 DOI:10.1007/s11464-011-0115-z

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Asaad M. On minimal subgroups of finite groups. Glasgow Mathematical Journal, 2009, 51, 359-366

[2]

Berkovich Y. Groups of Prime Power Order, Vol 1, 2008, Berlin: Walter de Gruyter.

[3]

Conway J. H., Curtis R. T., Norton S. P., Parker R. A., Wilson R. A. Atlas of Finite Groups, 1985, Oxford: Oxford University Press.

[4]

Doerk K. Minimal nicht überauflösbare, endliche Gruppen. Math Z, 1966, 91, 198-205

[5]

Itô N. Über die Frattini-Gruppe einer endlichen Gruppe. Proc Japan Acad, 1955, 31 6 327-328

[6]

King O. H. The subgroup structure of finite classical groups in terms of geometric configurations. Surveys in Combinatorics, 2005, Cambridge: Cambridge University Press 29-56

[7]

Li S. On minimal non-PE-groups. Journal of Pure and Applied Algebra, 1998, 132 2 149-158

[8]

Robinson D. J. S. A Course in the Theory of Groups, 1980, New York-Heidelberg-Berlin: Springer-Verlag.

[9]

Sastry N. S. N. On minimal nonPN-groups. Journal of Algebra, 1980, 65, 104-109

[10]

Schmidt O. J. Über Gruppen, deren sämtliche Teiler spezielle Gruppen sind. Mat Sbornik, 1924, 31, 366-372

[11]

Shaalan A., Ramadan M. On MNP-groups. Annales Univ Sci Budapest, 1993, 36, 23-30

[12]

Srinivasan S. Two sufficient conditions for supersolvability of finite groups. Israel Journal of Mathematics, 1980, 35, 210-214

[13]

Suzuki M. On a class of doubly transitive groups. Annals of Mathematics, 1962, 75 2 105-145

[14]

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

[15]

Zhang Q., Wang L., Guo P. On the structure of some finite groups. Southeast Asian Bulletin of Mathematics, 2006, 30, 995-1002

AI Summary AI Mindmap
PDF (96KB)

1280

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/