Define the axis of a loxodromic Möbius transformation acting on hyperbolic 3-space.

When do two loxodromic transformations commute? Justify your answer.

Let $G$ be a Kleinian group that contains a loxodromic transformation. Show that the fixed point of any loxodromic transformation in $G$ lies in the limit set of $G$. Prove that the set of such fixed points is dense in the limit set. Give examples to show that the set of such fixed points can be equal to the limit set or a proper subset.