A note on Frobenius quotient for prime-power divisor of the exponent of finite groups

Jiangtao Shi, Wenjing Liu

Let $G$ be a finite group and $n$ be any prime-power divisor of $\exp (G)$, the exponent of $G$. Frobenius' theorem indicates that $|\{g\in G\mid g^n=1\}|=f_n\cdot n$ for some…