1201.0978Jan 4, 2012This 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
A sufficient condition for finite presentability of abelian-by-nilpotent groups
Ralph Strebel
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.