On the measure of inclusion in relatively free algebras with the identity of Lie nilpotency of degree 3 or 4

This work is concerned with the concept of a graded subspace of the polylinear part of a relatively free algebra and with the measure of inclusion of such a subspace. Other asymptotic characteristics are also considered. In the case of relatively free algebras with the identity of Lie nilpotency of degree 3 and 4, the measure of inclusion is computed for many subspaces; in particular, for the centre and the $T$-space generated by the commutator this measure is $1/2$.
Bibliography: 17 titles.