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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

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[2] D. M. Smirnov, “Ob obobschenno razreshimykh gruppakh i ikh gruppovykh koltsakh”, DAN SSSR, 155:3 (1964), 535–537 | MR | Zbl

[3] F. Kholl, “Nilpotentnye gruppy”, Matematika, 12:1 (1968), 3–36 | MR

[4] E. M. Levich, “O predstavlenii razreshimykh grupp matritsami nad nekotorym polem kharakteristika nul”, Trudy Rizhskogo algebr. seminara, 1 (1969), 74–97

[5] M. I. Kargopolov, Yu. I. Merzlyakov, V. I. Remeslennikov, “O popolnenii grupp”, DAN SSSR, 134:3 (1960), 518–520 | MR