On the jet spaces \(J^k(\mathbb R^m,\mathbb R^n)\) product is defined, which turns then to Carnot groups. It is emphasized that this product gives rise to a contact structure which coincides with the classical contact structure in the Lie-Bäcklund setting. Therefore, by prolongation, they are nonrigid Carnot groups, i.e., the space of contact maps is infinite dimensional. It is shown that strata dimensions are not rigidity invariants. This is achieved by constructing two distinct Carnot groups with strata dimensions \((3,2,1)\), but with opposite rigidity.