Geodesic
On the homological dimension of group algebras of solvable groups
Izvestiya. Mathematics , Tome 5 (1971) no. 6, pp. 1231-1244

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In the paper we calculate the weak dimension of the group algebra of a solvable group and the projective dimension of the group algebra of a countable nilpotent group. Exact bounds are obtained for the projective dimension of the group algebra of a torsion-free solvable group. For the case that the principal ring is commutative and Noetherian we obtain corresponding results for global dimensions. On the assumption that the principal ring is a field we prove the additivity of projective and weak dimension on a class of groups for which there exists a finitely generated projective resolvent of the principal ring. 
@article{IM2_1971_5_6_a3,
     author = {G. L. Fel'dman},
     title = {On the homological dimension of group algebras of solvable groups},
     journal = {Izvestiya. Mathematics },
     pages = {1231--1244},
     publisher = {mathdoc},
     volume = {5},
     number = {6},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a3/}
}
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G. L. Fel'dman. On the homological dimension of group algebras of solvable groups. Izvestiya. Mathematics , Tome 5 (1971) no. 6, pp. 1231-1244. http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a3/