Some primitive linear groups of prime degree

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概要

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• 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.

• 社団法人 日本数学会の論文

著者

• Kang Ming-Chang

  National Taiwan University

• Zhang Ji-Ping

  Peking University

• Shi Jian-Yi

  East China Normal University

• YU Yung

  Cheng Kung University

• YAU Stephen

  University of Illinois at Chicago

関連論文

• Some primitive linear groups of prime degree
• Some primitive linear groups of prime degree

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