Abstract

We consider a Lie ring (algebra) L that admits an automorphism � of order 4 with a finite number m of fixed points (with a fixed-point subalgebra of finite dimension m). It is proved that L contains a subring S of m-bounded index in the additive group L (a subalgebra S of m-bounded codimension), which possesses a nilpotent ideal I of class bounded by some constant, such that the factor-ring S/I is nilpotent of class � 2. As a consequence, it is proved that, under the same conditions, L has a subring G of m-bounded index in the additive group of L (a subalgebra G of m-bounded codimension), in which an ideal generated by the Lie subring G, �2 = �-g+g �2 |g � G� (the subalgebra G, �2 = �-g+g�2 |g � G� is an ideal in G which) is nilpotent of class bounded by some constant (and its factor-algebra G/G, �2 is nilpotent of class � 2 with a derived algebra (square) of m-bounded dimension). In proofs, we use the results of 1 and develop further the version of the method of generalized centralizers employed therein. © 1998 Plenum Publishing Corporation.