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THE CLASSIFICATION OF SOME MODULAR FROBENIUS GROUPS

  • JUANJUAN FAN (a1), NI DU (a2) and JIWEN ZENG (a3)
Abstract
Abstract

Fix a prime number p. Let G be a p-modular Frobenius group with kernel N which is the minimal normal subgroup of G. We give the complete classification of G when N has three, four or five p-regular conjugacy classes. We also determine the structure of G when N has more than five p-regular conjugacy classes.

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Copyright
Corresponding author
For correspondence; e-mail: duni@xmu.edu.cn
Footnotes
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This research was supported by the Fundamental Research Funds for the Central Universities (No. 2010121003).

Footnotes
References
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[1]Alemany E., Beltrán A. and Felipe M. J., ‘Finite groups with two p-regular conjugacy class lengths II’, Bull. Aust. Math. Soc. 79 (2009), 419425.
[2]Dixon J. D. and Mortimer B., Permutation Groups (Springer, New York, 1996).
[3]Gallagher P. X., ‘The number of conjugacy classes in a finite group’, Math. Z. 118 (1970), 175179.
[4] The GAP Group, ‘GAP – Groups, Algorithms, and Programming’, Version 4.4, 2006, http://www.gap-system.org.
[5]Isaacs I. M., ‘Lifting Brauer characters of p-solvable groups’, Pacific J. Math. 53 (1974), 171188.
[6]Isaacs I. M., Character Theory of Finite Groups (Academic Press, New York, 1976).
[7]Kuisch E. B. and van der Waall R. W., ‘Modular Frobenius groups’, Manuscripta Math. 90 (1996), 403427.
[8]Kurzweil H. and Stellmacher B., The Theory of Finite Groups: An Introduction (Springer, New York, 2004).
[9]Navarro G., Characters and Blocks of Finite Groups (Cambridge University Press, Cambridge, 1978).
[10]Robinson D. J. S., A Course in the Theory of Groups (Springer, New York, Berlin, 2003).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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