Primary and biprimary class sizes implying nilpotency of finite groups

Authors: QINHUI JIANG, CHANGGUO SHAO

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

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