Geodesic
The variety of metabelian $\mathscr D$-groups
Izvestiya. Mathematics , Tome 6 (1972) no. 4, pp. 759-781

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It is proved that an arbitrary metabelian $R$-group is imbeddable in a metabelian $\mathscr D$-group. Varieties consisting of metabelian $\mathscr D$-groups are described and a number of theorems on the structure of a free metabelian $\mathscr D$-group are obtained. A certain specially defined ring – an analog of the group ring – plays an essential role in the proofs. 
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     author = {Yu. V. Kuz'min},
     title = {The variety of metabelian $\mathscr D$-groups},
     journal = {Izvestiya. Mathematics },
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     number = {4},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a4/}
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Yu. V. Kuz'min. The variety of metabelian $\mathscr D$-groups. Izvestiya. Mathematics , Tome 6 (1972) no. 4, pp. 759-781. http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a4/