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Some necessary and sufficient conditions for p-nilpotence of finite groups

Published online by Cambridge University Press:  17 April 2009

Huaquan Wei ,
Yanming Wang  and
Xiaolei Liu
Huaquan Wei
Affiliation:
School of Mathematics, Zhongshan University, Guangzhou, 510275, China and Deptartment of Mathematics, Guangxi Teacher's College, Nanning, 530001, China, e-mail: weihuaquan@163.com
Yanming Wang
Affiliation:
Lingnan College and School of Math., Zhongshan University, Guangzhou, 510275, China, email: stswym@zsu.edu.cn
Xiaolei Liu
Affiliation:
Lingnan College and School of Math., Zhongshan University, Guangzhou, 510275, China
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Abstract

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The purpose of this paper is to give some necessary and sufficient conditions for p-nilpotent groups. We extend some results, including the well-known theorems of Burnside and Frobenius as well as some very recent theorems. We also apply our results to determine the structure of some finite groups in terms of formation theory.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 371 - 378
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Burnside, W., ‘On some properties of groups of odd order’, Proc. London Math. Soc. 33 (1901), 257–268.Google Scholar
[2]Frobenius, F.G., ‘Über auflösbare Gruppen V’, S.-B. Preuss Akad. Berlin (1901), 1324–1329.Google Scholar
[3]Li, S., ‘On minimal subgroups of finite groups (III)’, Comm. Algebra 26 (1998), 2453–2461.Google Scholar
[4]Ballester-Bolinches, A. and Guo, X., ‘Some results on p-nilpotence and solubility of finite groups’, J. Algebra. 228 (2000), 491–496.CrossRefGoogle Scholar
[5]Guo, X. and Shum, K., ‘The influence of minimal subgroups of focal subgroups on the structure of finite groups’, J. Pure Appl. Algebra 169 (2002), 43–50.CrossRefGoogle Scholar
[6]Ballester-Bolinches, A. and Guo, X., ‘On complemented subgroups of finite groups’, Arch. Math. 72 (1999), 161–166.CrossRefGoogle Scholar
[7]Wang, Y., Wei, H. and Li, Y., ‘A generalization of a theorem of Kramer and its applications’, Bull. Austral. Math. Soc. 65 (2000), 467–475.CrossRefGoogle Scholar
[8]Dornhoff, L., ‘M-group and 2-groups’, Math. Z. 100 (1967), 226–256.CrossRefGoogle Scholar
[9]Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin, Heidelberg, New York, 1983).Google Scholar