Abstract: The problem of understanding the global symmetries of non-holonomic mechanical systems is quite difficult. One possible approach to tackle the problem from an algebraic point of view was proposed by N. Tanaka in the 70s, through the process known as (Tanaka) prolongation. The output of the prolongation is a graded Lie algebra, whose dimension is an upper bound for the dimension of the space of symmetries. A system is called rigid if its prolongation is finite dimensional. In this talk, I will show the generic rigidity of a wide class of non-holonomic systems of step 2 (so-called Carnot groups). This result was obtained in joint work with B. Kruglivok (Tromsø), I. Markina and A. Vasil'ev (Bergen).