On the nilpotent length of polycyclic groups (Q1265555)

Let \(G\) be a polycyclic group. The author proves that if the nilpotent length of each finite quotient of \(G\) is bounded by a fixed integer \(n\), then the nilpotent length of \(G\) is at most \(n\). As a consequence, it is obtained that if the nilpotent length of each 2-generator subgroup is at most \(n\), then the nilpotent length of \(G\) is at most \(n\). In the case \(n=2\), the author shows that if each 3-generator subgroup is Abelian-by-nilpotent, then \(G\) is Abelian-by-nilpotent. Also, it is proved that the nilpotent length of \(G\) equals the nilpotent length of the quotient of \(G\) by its Frattini subgroup.