The structure of differential invariants for a free symmetry group action

In the paper, we consider the problem of describing the general structure of differential invariants for transformation groups that act freely and reguralry. We formulate two theorems describing the structures of differential invariants for intransitive and transitive free actions, respectively. In both cases it is shown that the differential invariants can be expressed in terms of the symbols of right-invariant vector fields. Finally, we discuss prospects for solving the problem considered for more general group actions.