Characterization of PGL(2, ð?‘?) by its order and one conjugacy class size

Proceedings Mathematical Sciences

Yanheng Chen²  Guiyun Chen¹ 

[1] School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 000, People's Republic of China$$;School of Mathematics and Statistics, Southwest University, Chongqing 00, People's Republic of China$$

关键词: Finite group;    conjugacy class size;    Thompson's conjecture.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let 𝑝 be a prime. In this paper, we do not use the classification theorem of finite simple groups and prove that the projective general linear group PGL(2, 𝑝) can be uniquely determined by its order and one special conjugacy class size. Further, the validity of a conjecture of J. G. Thompson is generalized to the group PGL(2, 𝑝) by a new way.

【 授权许可】

Unknown