Geodesic
On~the representation of metabelian groups by matrices over a~field of characteristic zero
Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 327-332

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It is proved that every metabelian torsion-free group with finitely many generators admits a faithful matrix representation over a field of characteristic zero. Bibliography: 5 titles. 
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     author = {E. M. Levich},
     title = {On~the representation of metabelian groups by matrices over a~field of characteristic zero},
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E. M. Levich. On~the representation of metabelian groups by matrices over a~field of characteristic zero. Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 327-332. http://geodesic.mathdoc.fr/item/SM_1970_10_3_a2/