Modules of type FP2 over the integral group algebra of a metabelian group

摘要

We establish a sufficient condition for some modules M over the group algebra Z[G] to be of homological type FP2, where G is a finitely generated split extension of abelian groups. This generalizes a result of Bieri and Strebel [6] when M is the trivial module Z and it establishes a special case of [10, Conjecture 7].