Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 61, Number 4 (2009), 1013-1070.
Some primitive linear groups of prime degree
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 up to conjugation for some small values of . This question is important in group theory as well as in the study of quotient singularities. Some results of Blichfeldt when were generalized to the case of finite primitive subgroups of and by Brauer and Wales. The purpose of this article is to consider the following case. Let be any odd prime number and be a finite primitive subgroup of containing a non-trivial monomial normal subgroup so that has a non-scalar diagonal matrix. We will classify all these groups up to conjugation in by exhibiting the generators of and representing as some group extensions. In particular, see the Appendix for a list of these subgroups when or 7.
J. Math. Soc. Japan, Volume 61, Number 4 (2009), 1013-1070.
First available in Project Euclid: 6 November 2009
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Zentralblatt MATH identifier
Primary: 20C15: Ordinary representations and characters
KANG, Ming-chang; ZHANG, Ji-ping; SHI, Jian-yi; YU, Yung; YAU, Stephen S. T. Some primitive linear groups of prime degree. J. Math. Soc. Japan 61 (2009), no. 4, 1013--1070. doi:10.2969/jmsj/06141013. https://projecteuclid.org/euclid.jmsj/1257520499