Geodesic
Projective metabelian groups and Lie algebras
Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 213-223

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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. 
@article{IM2_1978_12_2_a1,
     author = {V. A. Artamonov},
     title = {Projective metabelian groups and {Lie} algebras},
     journal = {Izvestiya. Mathematics },
     pages = {213--223},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a1/}
}
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V. A. Artamonov. Projective metabelian groups and Lie algebras. Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 213-223. http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a1/