# Frobenius conjecture on nth roots

## Statement

Suppose $G$ is a finite group and $n$ is a natural number dividing the order of $G$. Suppose the number of $n^{th}$ roots in $G$, i.e., the number of elements $g \in G$ such that $g^n = e$, is exactly $n$.

The Frobenius conjecture on nth roots states that in that case, that set of $n^{th}$ roots must be a subgroup of $G$.