A sufficient condition for finite presentability of abelian-by-nilpotent groups

Abstract

A recipe for obtaining finitely presented abelian-by-nilpotent groups is given. It relies on a geometric procedure that generalizes the construction of finitely presented metabelian groups introduced by R. Bieri and R. Strebel in 1980.

arXiv commentThis second version takes into account the suggestions by the referee; it includes, in particular, an additional Section 5 giving some examples and a necessary condition for the finite presentability of abelian-by-nilpotent groups; 27 pages