• Conjugacy Class Sizes and Solvability of Finite Groups

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/123/02/0239-0244

• # Keywords

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

• # Abstract

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).

• # Author Affiliations

1. School of Mathematical Sciences, University of Jinan, Shandong 250022, China

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019