Let $\displaystyle H\leq G$. Show that $\displaystyle H\leq N_G(h)$. Give an example to show that this is not necessarily true if H is not a subgroup.

Since H is a subgroup e is in H. $\displaystyle e=xx^{-1}$ so $\displaystyle x,x^{-1}\in H$.

How can I show the proposition?