Maximum principle and propagation for intrinsicly regular solutions of differential inequalities structured on vector fields

We prove suitable versions of the weak maximum principle and of the maximum propagation for solutions u of a differential inequality Hu⩾0. Here H=∑i,jai,j(z)ZiZj+Z0 is a differential operator structured on the vector fields Zj's, whereas u belongs to an appropriate intrinsic class of regularity modelled on the Zj's.