Projective metabelian groups and Lie algebras

Suppose that $A_n$ is the variety of all abelian groups of exponent dividing $n\geqslant0$, and $A_n=A$ is the variety of all abelian groups. In this paper it is proved that projective metabelian $A_nA$-groups of finite rank are free. Moreover, it is proved that projective metabelian $k[Y_1^{\pm1},\dots,Y_r^{\pm1},Z_1,\dots,Z_s]$-Lie algebras of finite rank, where $k$ is a principal ideal ring, are free.
Bibliography: 9 titles.