I'm sorry for my simple question, however i've started a sort of review on the theory of finite group, and i've to admit i'm really rusted, even though i've never really been brilliant in this subject.
However the question is the following:
Let $G$ be a finite group and $H\leq G$.
Show that $|N_G(H):H|$ is equal to the number of right cosets of $H$ in $G$ that are invariant under right multiplication by $H$. (i was able to solve this part)
Suppose now that $|H|$ is a power of the prime $p$ and that $|G:H|$ is divisible by $p$. Show that $|N_G(H):H|$ is divisible by $p$.