Primary and biprimary class sizes implying nilpotency of finite groups

Authors

QINHUI JIANG
CHANGGUO SHAO

DOI

10.3906/mat-1504-79

Abstract

Let $G$ be a finite group. We prove that $G$ is nilpotent if the set of conjugacy class sizes of primary and bipirimary elements is $\{1,m,n,mn\}$ with $m$ and $n$ coprime. Moreover, $m$ and $n$ are distinct primes power.

Keywords

Finite groups, conjugacy class sizes, primary and biprimary elements

First Page

389

Last Page

396

Recommended Citation

JIANG, QINHUI and SHAO, CHANGGUO (2016) "Primary and biprimary class sizes implying nilpotency of finite groups," Turkish Journal of Mathematics: Vol. 40: No. 2, Article 13. https://doi.org/10.3906/mat-1504-79
Available at: https://journals.tubitak.gov.tr/math/vol40/iss2/13