TheFPm-Conjecture for a Class of Metabelian Groups Original Research Article

We prove that ifA→G→Qis a short exact sequence of groups whereGis finitely generated,AandQare abelian,Ais a2-torsion Krull dimension one3Q-module via conjugation then theFPm-Conjecture holds. In general ifGis of typeFPmand either the extension is split orAis4-torsion we show thatAism-tame as5Q-module.