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October, 2009 Some primitive linear groups of prime degree
Ming-chang KANG, Jian-yi SHI, Stephen S. T. YAU, Yung YU, Ji-ping ZHANG
J. Math. Soc. Japan 61(4): 1013-1070 (October, 2009). DOI: 10.2969/jmsj/06141013


A classical problem in finite group theory dating back to Jordan, Klein, E. H. Moore, Dickson, Blichfeldt etc. is to determine all finite subgroups in SL ( n , C ) up to conjugation for some small values of n . This question is important in group theory as well as in the study of quotient singularities. Some results of Blichfeldt when n = 3 , 4 were generalized to the case of finite primitive subgroups of SL ( 5 , C ) and SL ( 7 , C ) by Brauer and Wales. The purpose of this article is to consider the following case. Let p be any odd prime number and G be a finite primitive subgroup of SL ( p , C ) containing a non-trivial monomial normal subgroup H so that H has a non-scalar diagonal matrix. We will classify all these groups G up to conjugation in SL ( p , C ) by exhibiting the generators of G and representing G as some group extensions. In particular, see the Appendix for a list of these subgroups when p = 5 or 7.


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Ming-chang KANG. Jian-yi SHI. Stephen S. T. YAU. Yung YU. Ji-ping ZHANG. "Some primitive linear groups of prime degree." J. Math. Soc. Japan 61 (4) 1013 - 1070, October, 2009.


Published: October, 2009
First available in Project Euclid: 6 November 2009

zbMATH: 1211.20040
MathSciNet: MR2588503
Digital Object Identifier: 10.2969/jmsj/06141013

Primary: 20C15

Keywords: linear groups of prime degree , monomial groups

Rights: Copyright © 2009 Mathematical Society of Japan


Vol.61 • No. 4 • October, 2009
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