On the minimal generator number of a polycyclic nilpotent-by-finite group

Abstract

The determination of the minimal generator number d(G) of a polycyclic group G is one of the few still open problems in the algorithmic theory of these groups. If \(\hat{G}\) is the profinite completion of G, then it is known that \(d(G) = d(\hat{G})\) or \(d(G) = d(\hat{G}) +1\) holds. The aim here is to introduce a construction for \(d(\hat{G})\) if G is polycyclic and nilpotent-by-finite.