Conjugacy Class Sizes and Solvability of Finite Groups

Proceedings Mathematical Sciences

Qinhui Jiang²  Changguo Shao¹ 

[1] $$;School of Mathematical Sciences, University of Jinan, Shandong 00, China$$

关键词: Conjugacy class sizes;    primary;    biprimary and triprimary elements;    solvable groups;    finite groups.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let 𝐺 be a finite group and 𝐺* be the set of primary, biprimary and triprimary elements of 𝐺. We prove that if the conjugacy class sizes of 𝐺* are {1,𝑚,𝑛,𝑚𝑛} with positive coprime integers 𝑚 and 𝑛,then 𝐺 is solvable. This extends a recent result of Kong (Manatsh. Math. 168(2)(2012) 267–271).

【 授权许可】

Unknown