Abstract
The homological invariant Sigma^1(G), where G is afinitely generated metabelian group, was used to classify finitely presentable metabelian groups. The description of such groups was based in the geometric properties of Sigma^1(G). The FPm-Conjecture relates geometric properties of this invariant with the homological type FPm of G. The FP3-Conjecture was proved when G is a split extensio…