Acta mathematica scientia, Series B >
CHARACTERIZATION OF MODULAR FROBENIUS GROUPS OF SPECIAL TYPE
Received date: 2011-02-25
Revised date: 2012-10-20
Online published: 2013-03-20
Supported by
Supported by the National Natural Science Foun-dation of China (11171243, 11201385), the Technology Project of Department of Education of Fujian Province (JA12336), the Fundamental Research Funds for the Central Universities (2010121003), and the Science and the Natural Science Foundation of Fujian Province (2011J01022).
In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G′ is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of G when G′ as a modular Frobenius kernel has no more than four conjugacy classes in G.
FAN Juan-Juan , DU Ni , ZENG Ji-Wen . CHARACTERIZATION OF MODULAR FROBENIUS GROUPS OF SPECIAL TYPE[J]. Acta mathematica scientia, Series B, 2013 , 33(2) : 525 -531 . DOI: 10.1016/S0252-9602(13)60016-8
[1] Kuisch E B, van der Waall R W. Modular Frobenius groups. Manuscripta Math, 1996, 90: 403–427
[2] Riese U, Shahabi M A. Subgroups which are the union of four conjugacy classes. Comm Algebra, 2001, 29: 695–701
[3] Shahryari M, Shahabi M A. Subgroups which are the union of three conjugate classes. J Algebra, 1998, 207: 326–332
[4] Shahryari M, Shahabi M A. Subgroups which are the union of two conjugate classes. Bull Iran Math Soc, 1999, 25: 59–71
[5] Navarro G. Characters and Blocks of Finite Groups. Cambridge: Cambridge University Press, 1998
[6] Isaacs I M. Character Theory of Finite Groups. New York: Academic Press, 1976
[7] Isaacs I M. Lifting Brauer characters of p-solvable groups. Pacific J Math, 1974, 53: 171–188
[8] Camina A R. Some conditions which almost characterize Frobenius groups. Isr J Math, 1978, 31: 153–160
[9] Robinson D J S. A Course in the Theory of Groups. New York, Berlin: Springer, 2003
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