Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T07:14:18.949Z Has data issue: false hasContentIssue false
  • English
  • Français

ON MINIMAL SUBGROUPS OF FINITE GROUPS

Published online by Cambridge University Press:  01 May 2009

M. ASAAD
M. ASAAD*
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt e-mail: moasmo45@hotmail.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a finite group. A minimal subgroup of G is a subgroup of prime order. A subgroup of G is called S-quasinormal in G if it permutes with each Sylow subgroup of G. A group G is called an MS-group if each minimal subgroup of G is S-quasinormal in G. In this paper, we investigate the structure of minimal non-MS-groups (non-MS-groups all of whose proper subgroups are MS-groups).

Keywords

20D1020D20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 2 , May 2009 , pp. 359 - 366
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Asaad, M. and Csörgö, P., The influence of minimal subgroups on the structure of finite groups, Arch. Math. 72 (1999), 401–404CrossRefGoogle Scholar
2.Doerk, K., Minimal nicht überauflösbare, endliche Gruppen, Math. Z. 91 (1966), 198–205.CrossRefGoogle Scholar
3.Doerk, K. and Hawkes, T., Finite solvable groups (Walter de Gruyter, Berlin/New York, 1992).Google Scholar
4.Gorenstein, D., Finite groups (Harper Row, New York, 1968).Google Scholar
5.Huppert, B., Endliche gruppen I (Springer-Verlag, Berlin/New York, 1967).Google Scholar
6.Huppert, B. and Blackburn, N., Finite groups III (Springer-Verlag, Berlin/New York, 1982).Google Scholar
7.Kegel, O. H., Sylow-Gruppen und Subnormalteiler endlicher Gruppen, Math. Z. 78 (1962), 205–221.CrossRefGoogle Scholar
8.Sastry, N. S. N., On minimal non-PN-groups, J. Algebra 65 (1980), 104–109.CrossRefGoogle Scholar
9.Schmidt, O. J., Über Gruppen, deren sämtliche Teiler spezielle Gruppen sind, Mat. Sbornik 31 (1924), 366–372.Google Scholar
10.Thompson, J. G., Nonsolvable finite groups all of whose local subgroups are solvable I, Bull. Amer. Math. Soc. 74 (1968), 383–437.Google Scholar