Frobenius's theorem (group theory)

In mathematics, specifically group theory, Frobenius's theorem states that if ${\displaystyle n}$ divides the order of a finite group ${\displaystyle G}$, then the number of solutions of ${\displaystyle x^{n}=1}$ in ${\displaystyle G}$ is a multiple of ${\displaystyle n}$. It was introduced by Frobenius (1903).