Hi everyone.

Let $\displaystyle N$ be a normal subgroup of $\displaystyle G$ of finite index $\displaystyle n$. Given an element $\displaystyle t\in{G}$, let $\displaystyle h$ be the least positive integer such that $\displaystyle t^h\in{N}$. Prove that $\displaystyle h|n$; also show that, if $\displaystyle t$ is if finite order $\displaystyle r$, then $\displaystyle h|r$

Thanks.