I am trying to prove: for $H$ a subgroup of $G$ and $g$ an element of $G$
$N_{G}(gHg^{-1})=gN_{G}(H)g^{-1}$
I have started along these lines:
let $x$ be an element of $N_{G}(gHg^{-1})$
therefore $x$ is an element of $G$ such that
$x(gHg^{-1})x^{-1}=gHg^{-1}$
and then I'm confused as to how to go from here.
please help.