In a group of permutations of $n$ elements, there are two permutations $P_1$ and $P_2$ such that $P_2=P_1^e$. $P_1$ and $P_2$ have the same order $o$: $P_1^o = P_2^o$. How can I find $e$?
$n$, $P_1, P_2$ and $o$ are known, $e$ is not known. Problem is to find $e$.