In the theory of associative rings various authors have investigated the connection between the rings R G and R. An important theorem in this direction was proved in [i]: If the ring R is iGl-torsion-free (G a finite group of automorphisms of R), then nilpotency of R G implies nilpotency of R. It was shown in [2] that, under the same conditions, if R G is a PI-ring, then R is a PI-ring. In nonassociative rings, mainly regular (i.e., having no fixed points) automorphisms of finite orders have been studied [3, 4]. We must mention the paper [5], in which were investigated the connections between properties of R G and R in the case where G is a finite group of Jordan automorphisms of an associative ring R.