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On c-normality of finite groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

M. Asaad  and
M. Ezzat Mohamed
M. Asaad
Affiliation:
Cairo UniversityFaculty of Science Department of Mathematics GizaEgypt e-mail: moasmohs@frcu.eun.eg
M. Ezzat Mohamed
Affiliation:
Cairo UniversityFaculty of Science Department of Mathematics GizaEgypt e-mail: moasmohs@frcu.eun.eg
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Abstract

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A subgroup H of a finite G is said to be c-normal in G if there exists a normal subgroup N of G such that G = HN with H ∩ N ≤ HG = CoreG(H). We are interested in studying the influence of the c–normality of certain subgroups of prime power order on the structure of finite groups.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D30: Series and lattices of subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 3 , June 2005 , pp. 297 - 304
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Asaad, M., ‘On maximal subgroups of Sylow subgroups of finite groups’, Comm. Algebra 26 (1998), 3647–3652.CrossRefGoogle Scholar
[2]Asaad, M. and Csörgö, P., ‘The influence of minimal subgroups on the structure of finite groups’, Arch. Math. 72 (1999), 401–404.CrossRefGoogle Scholar
[3]Derr, J. B., Deskins, W. E. and Mukherjee, N. P., ‘The influence of minimal p–subgroups on the structure of finite groups’, Arch. Math. 45 (1985), 1–4.CrossRefGoogle Scholar
[4]Deyu, L. and Xiuyun, G., ‘The influence of c-normality of subgroups on the structure of finite groups II’, Comm. Algebra 26 (1998), 1913–1922.CrossRefGoogle Scholar
[5]Doerk, K. and Hawkes, T., Finite soluble groups (Walter De Gruyter, Berlin, 1992).CrossRefGoogle Scholar
[6]Huppert, B., Endliche Gruppen I (Springer, Berlin, 1967).CrossRefGoogle Scholar
[7]Huppert, B., ‘Zur Theorie der Formationen’, Arch. Math. 19 (1968), 561–574.CrossRefGoogle Scholar
[8]Ito, N., ‘Uber eine zur Frattini. Gruppe duale Bildung’, Nagoya Math. J. 9 (1955), 123–127.CrossRefGoogle Scholar
[9]Kegel, O. H., ‘Sylow-Gruppen und Subnormalteiler endlicher Gruppen’, Math. Z. 78 (1962), 205–221.CrossRefGoogle Scholar
[10]Shaalan, A., ‘The influence of S-quasinormality of some subgroups on the structure of a finite group’, Acta Math. Hungar. 56 (1990), 287–293.CrossRefGoogle Scholar
[11]Wang, Y., ‘C-normality of groups and its properties’, J. Algebra 180 (1996), 954–965.CrossRefGoogle Scholar
[12]Weinstein, M. (ed.), Between nilpotent and solvable (Polygonal Publ. H., Washington, 1982).Google Scholar
[13]Xiuyun, G. and Deyu, L., ‘The influence of c-normality of subgroups on the structure of finite groups’, J. Pure Appl. Algebra 150 (2000), 53–60.Google Scholar