Finite Groups with Three Conjugacy Class Sizes of some Elements

Proceedings Mathematical Sciences

Qingjun Kong¹ 

[1] Department of Mathematics, Tianjin Polytechnic University, Tianjin 000, People’s Republic of China$$

关键词: Conjugacy class sizes;    𝑝-nilpotent 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. We prove as follows: Let 𝐺 be a 𝑝-solvable group for a fixed prime 𝑝. If the conjugacy class sizes of all elements of primary and biprimary orders of 𝐺 are ${1,p^a,n}$ with 𝑎 and 𝑛 two positive integers and (𝑝,𝑛)=1, then 𝐺 is 𝑝-nilpotent or 𝐺 has abelian Sylow 𝑝-subgroups.

【 授权许可】

Unknown