Geodesic
Faithful Representations of Finitely Generated Metabelian Groups
Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1355-1360

Voir la notice de l'article provenant de la source Cambridge University Press

In [3] Remeslennikov proves that a finitely generated metabelian group G has a faithful representation of finite degree over some field F of characteristic zero (respectively, p > 0) if its derived group G’ is torsion-free (respectively, of exponent p). By the Lie-Kolchin-Mal'cev theorem any metabelian subgroup of GL(n, F) has a subgroup of finite index whose derived group is torsion-free if char F = 0 and is a p-group of finite exponent if char F = p > 0. Moreover every finite extension of a group with a faithful representation (of finite degree) has a faithful representation over the same field. Thus Remeslennikov's results have a gap which we propose here to fill. 
Wehrfritz, B. A. F. Faithful Representations of Finitely Generated Metabelian Groups. Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1355-1360. doi: 10.4153/CJM-1975-138-0
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[1] 1. Cohen, I. S., On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc. 59 (1946), 54–106. Google Scholar

[2] 2. Remeslennikov, V. N., Finite approximability of metabelian groups (Russian), Alg. i Logika 7 (1968), 106-113; Alg. and Logic 7 (1968), 268–272. Google Scholar

[3] 3. Remeslennikov, V. N., Representations of finitely generated metabelian groups by matrices (Russian), Alg. i Logika 8 (1969), 72-75; Alg. and Logic 8 (1969), 39–40 Google Scholar

[4] 4. Wehrfritz, B. A. F., Infinite linear groups, Ergeb. d. Math. Bd. 76 (Springer-Berlin Heidelberg New York, 1973). Google Scholar

[5] 5. Zariski, O. and Samuel, P., Commutative algebra Vol. 1 (Van Nostrand-Princeton, 1958). Google Scholar

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