Plane torsion waves in quadratic gravitational theories in Riemann-Cartan space

The definition of the Riemann-Cartan space of plane-wave type is given. The condition under which the torsion plane waves exist is found. It is expressed in the form of the restriction imposed on the coupling constants of the 10-parametric quadratic gravitational Lagrangian. In the mathematical appendix the master formula for the commutator of the variation operator and Hedge operator is proved. This formula is applied for the variational procedure when the gravitational field equations are obtained in terms of the exterior differential forms.