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FINITE GROUPS WITH SOME WEAKLY S-SUPPLEMENTED SUBGROUPS

Published online by Cambridge University Press:  08 December 2010

WENBIN GUO ,
K. P. SHUM  and
FENGYAN XIE
WENBIN GUO
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei 230026, China e-mail: [email protected]
K. P. SHUM
Affiliation:
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China e-mail: [email protected]
FENGYAN XIE
Affiliation:
Humanistic Management College, Anyang Normal University, Anyang 455000, China e-mail: [email protected]
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Abstract

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Let H be a subgroup of a group G. Then, we call H weakly s-supplemented in G if G has a subgroup T such that HT = G and H ∩ T ≤ HsG, where HsG is the largest s-permutable subgroup of G contained in H. In this paper, we use the weakly s-supplemented subgroups to characterize the structure of groups. A series of known results in the literature are unified and generalized.

Keywords

20D1020D25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 2 , May 2011 , pp. 211 - 222
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Ballester-Bolinches, A. and Wang, Y., Finite groups with some c-normal minimal subgroups, J. Pure Appl. Algebra 153 (2000), 121–127.CrossRefGoogle Scholar
2.Buckley, J., Finite groups whose minimal subgroups are normal, Math. Z. 116 (1970), 15–17.CrossRefGoogle Scholar
3.Doerk, K. and Hawkes, T., Finite solvable groups (Walter de Gruyter, New York, 1992).CrossRefGoogle Scholar
4.Guo, W., The influence of minimal subgroups on the structure of finite groups, Southeast Asian Bull. Math. 22 (1998), 287–290.Google Scholar
5.Guo, W., The Theory of classes of groups (Science Press-Kluwer Academic Publishers, Beijing–New York–Dordrecht–Boston–London, 2000).Google Scholar
6.Huppert, B., Endliche Gruppen I (Springer, Berlin–Heidelberg–New York, 1979).Google Scholar
7.Huppert, B. and Blackburn, N., Finite groups III (Springer, Berlin–New York, 1982).CrossRefGoogle Scholar
8.Lam, C. M., Shum, K. P. and Guo, W., A generalized Ito theorem on p-nilpotent groups, Pure Math. Appl. 11 (2000), 593–596.Google Scholar
9.Li, Y., Some notes on the minimal subgroups of Fitting subgroups of finite groups, J. Pure Appl. Algebra 171 (2002), 289–294.Google Scholar
10.Li, Y. and Wang, Y., On π-quasinormally embedded subgroups of finite group, J. Algebra 281 (2004), 109–123.CrossRefGoogle Scholar
11.Miao, L., W. Guo and Shum, K. P., New criteria for p-nilpotency of finite groups, Commun. Algebra 35 (2007), 965–974.CrossRefGoogle Scholar
12.Ramadan, M., Mohamed, M. E. and Heliel, A. A., On c-normality of certain subgroups of prime power order of finite groups, Arch. Math. 85 (2005), 203–210.CrossRefGoogle Scholar
13.Robinson, D. J. S., A Course in theory of group (Spinger, New York, 1982).CrossRefGoogle Scholar
14.Shemetkov, L. A., Formations of finite groups (Nauka, Moscow, 1978).Google Scholar
15.Skiba, A. N., On weakly s-permutable subgroups of finite groups, J. Algebra 315 (2007), 192–209.CrossRefGoogle Scholar
16.Wang, Y., c-Normality of groups and its properties, J. Algebra 180 (1996), 954–965.CrossRefGoogle Scholar
17.Wang, Y., The influence of minimal subgroups on the structure of finite group, Acta. Math. Sinica (English series) 16 (2000), 63–70.CrossRefGoogle Scholar
18.Wang, Y., Finite groups with some subgroup of Sylow subgroups c-supplemented, J. Algebra 224 (2000), 467–478.CrossRefGoogle Scholar
19.Wang, Y., Li, Y. and Wang, J., Finite groups with c-supplemented minimal subgroups, Algebra Colloquium 10 (3) (2003), 413–425.Google Scholar
20.Weinstein, M. (Editor), in Between Nilpotent and Solvable (Bray, H. G., Deskins, W. E., Johnson, D., Humphreys, J. F., Puttaswamaiah, B. M., Venzke, P. and Walls, G. L., Editors) (Polygonal Publishing House, NJ, USA, 1982).Google Scholar
21.Xie, F., Shi, L. and Hu, B., Some new criteria for p-nilpotency of finite groups, Math. Sci. Res. J. 12 (2) (2008), 38–43.Google Scholar
22.Zhong, X. and Li, S., On c-supplemented minimal subgroups of finite groups, Southeast Asian Bull. Math. 28 (2004), 1141–1148.Google Scholar