Comparison principles for degenerate sub-elliptic equations in non-divergence form

We prove the comparison principle for viscosity sub/super-solutions of degenerate subelliptic equations in non-divergence form that include the sub-elliptic infinity Laplacian and the normalized p-Laplacian. The equations are defined by a collection of vector fields satisfying Hörmander’s rank condition and are left invariant with respect to a nilpotent Lie Group.