Possible Duplicate:
$gHg^{-1}\subset H$ whenever $Ha\not = Hb$ implies $aH\not =bH$
Suppose that $H$ is a subgroup of $G$ such that whenever $H\circ a\neq H\circ b $ then $ a\circ H\neq b\circ H$.
Prove that $ g\circ H\circ g^{-1} \subset H$, $\forall g \in G$.