Finite extensions of A-solvable abelian groups

An abelian group G is almost A-solvable if the natural map theta (G): Hom(A , G)X(E(A))A --> G is a quasi-isomorphism. Two strongly indecomposable tors ion-free abelian groups A and B of finite rank are quasi-isomorphic if and only if the classes of almost A-solvable and almost B-solvable groups coinc ide. Homological properties of almost A-solvable groups are described, and several examples are given. In particular, there exists a torsion-free almo st A-solvable group which is not quasi-isomorphic to an A-solvable group. ( C) 2001 Elsevier Science B.V. All rights reserved.