  We extend Bony's propagation of support argument \cite{Bony} to $C^1$
solutions of the non-homogeneous sub-elliptic $p-$Laplacian associated to a
system of smooth vector fields satisfying H\"ormander's finite rank condition.
As a consequence we prove a strong maximum principle and strong comparison
principle that generalize results of Tolksdorf \cite{Tolksdorf}.
