Some finitely presented nilpotent-by-abelian groups (Q1178884)

The author gives some sufficient conditions for the finite presentability of nilpotent-by-abelian groups in geometric notions due to Bieri and Strebel. This is a generalization of a theorem by McIsaac who proved similar assertions for split extensions of a group of nilpotency class 2 by an abelian group. The restrictions on splitting and class 2 are removed now. Some examples are presented to show that the given conditions are not necessary.