Permutable quasiregular maps

Let $f$ and $g$ be two quasiregular maps in $\mathbb{R}^d$ that are of transcendental type also satisfy $f\circ g =g \circ f$. We show if the fast escaping sets those functions contained their respective Julia then must have same set. obtain conclusion about commuting quasimeromorphic with infinite backward orbit infinity. Furthermore we permutable form $g=\phi\circ f$, where $\phi$ is a quasiconformal map, polynomial cannot commute ones unless degree less than or equal to dilatation.