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ON SS-SUPPLEMENTED SUBGROUPS OF FINITE GROUPS AND THEIR PROPERTIES

Published online by Cambridge University Press:  30 March 2012

XIUYUN GUO  and
JIAKUAN LU
XIUYUN GUO
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China e-mail: xyguo@shu.edu.cn
JIAKUAN LU
Affiliation:
Department of Mathematics, Guangxi Normal University, Guilin 541004, Guangxi, P.R. China
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Abstract

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A subgroup H of a finite group G is called SS-supplemented in G if there exists a subgroup K of G such that HK = G and H ∩ K is S-quasinormal in K. In this paper, we characterize the finite groups in which every subgroup is SS-supplemented and the influence of SS-supplementation of some subgroups on the structure of finite groups is considered. Some recent results on SS-quasinormal subgroups and C-supplemented subgroups are strengthened and enriched.

Keywords

20D1020D20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 3 , September 2012 , pp. 481 - 491
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

1.Asaad, M. and Shaalan, A., On supersolvablility of finite groups, Arch. Math. 53 (1989), 318–326.CrossRefGoogle Scholar
2.Asaad, M., On maximal subgroups of Sylow subgroups of finite groups, Comm. Algebra 26 (1998), 3647–3652.Google Scholar
3.Baer, R., Classes of finite groups and their properties, Illinois J. Math. 1 (1957), 115–187.Google Scholar
4.Ballester-Bolinches, A., Cossey, J. and Pedraza-Aguilera, M. C., On products of finite supersoluble groups, Comm. Algebra 29 (2001), 3145–3152.Google Scholar
5.Ballester-Bolinches, A. and Guo, X., On complemented subgroups of finite groups, Arch. Math. 72 (1999), 161–166.CrossRefGoogle Scholar
6.Ballester-Bolinches, A. and Pérez-Ramos, M. D., A question of R. Maier concerning formations, J. Algebra 182 (1996), 738–747.CrossRefGoogle Scholar
7.Ballester-Bolinches, A., Wang, Y. and Guo, X., C-supplemented subgroups of finite groups, Glasgow Math. J. 42 (2000), 383–389.Google Scholar
8.Doerk, K. and Hawkes, T., Finite soluble groups (Walter de Gruyter, Berlin, 1992).CrossRefGoogle Scholar
9.Gorenstein, D., Finite groups (Harper & Row, New York, 1968).Google Scholar
10.Gross, F., Conjugacy of odd order Hall subgroups, Bull. London Math. Soc. 19 (1987), 311–319.Google Scholar
11.Guo, X. and Shum, K. P., The influence of minimal subgroups of focal subgroups on the structure of finite groups, J. Pure Appl. Algebra 169 (1) (2002), 43–51.Google Scholar
12.Guo, X. and Shum, K. P., Complementarity of subgroups and the structure of finite groups, Algebra Colloquium 13 (1) (2006), 9–16.Google Scholar
13.Guo, X. and Shum, K. P., Finite p-nilpotent groups with some subgroups c-supplemented, J. Aust. Math. Soc. 78 (3) (2005), 429–439.CrossRefGoogle Scholar
14.Hall, P., A characteristic property of soluble groups, J. London Math. Soc. 12 (1937), 198–200.Google Scholar
15.Hall, P., Complemented groups, J. London Math. Soc. 12 (1937), 201–204.Google Scholar
16.Huppert, B., Endliche Gruppen I (Springer-Verlag, New York, Berlin, 1967).Google Scholar
17.Itô, N., Über das Produkt von zwei abelschen Gruppen, Math. Z. 62 (1955), 400–401.Google Scholar
18.Kegel, O. H., Produkte nilpotenter Gruppen, Arch. Math. 12 (1961), 90–93.Google Scholar
19.Kegel, O. H., Sylow-Gruppen and Subnormalteiler endlicher Gruppen, Math. Z. 78 (1962), 205–221.Google Scholar
20.Levchuk, V. M. and Likharev, A. G., Finite simple groups with complement maximal sugroups, Siberian Math. J. 47 (4) (2006), 659–668.Google Scholar
21.Li, S., Shen, Z., Liu, J. and Liu, X., The influence of SS-quasinormality of some subgroups on the structure of finite groups, J. Algebra 319 (2008), 4275–4287.CrossRefGoogle Scholar
22.Li, S., Shen, Z. and Kong, X., On SS-quasinormal subgroups of finite groups, Comm. Algebra 36 (2008), 4436–4447.CrossRefGoogle Scholar
23.Maier, R., A completeness property of certain formations, Bull. London Math. Soc. 24 (1992), 540–544.CrossRefGoogle Scholar
24.Schmid, P., Subgroups permutable with all Sylow subgroups, J. Algebra 207 (1998), 285–293.Google Scholar
25.Skiba, A. N., On weakly s-permutable subgroups of finite groups, J. Algebra 315 (2007), 192–209.Google Scholar
26.Wang, Y., Wei, H. and Li, Y., A generalization of Kramer's theorem and its applications, Bull. Aus. Math. Soc. 65 (2002), 2193–2200.Google Scholar
27.Wei, H., Wang, Y. and Li, Y., On c-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups, Proc. Amer. Math. Soc. 132 (2004), 2197–2204.Google Scholar
28.Wielandt, H., Über den normalisator der subnormalen untergruppen, Math. Z. 69 (1958), 463–465.Google Scholar
29.Wielandt, H., Über Produkte von nilpotenten gruppen, Illinois J. Math. 2 (1958), 611–618.Google Scholar