‎we pursue further our‎ ‎investigation‎, ‎begun in [h.~smith‎, ‎groups with all subgroups subnormal or‎ ‎nilpotent-by-{c}hernikov‎, ‎emph{rend‎. ‎sem‎. ‎mat‎. ‎univ‎. ‎padova}‎ ‎126 (2011)‎, ‎245--253] and continued in [g.~cutolo and h.~smith‎, ‎locally finite groups with all subgroups‎ ‎subnormal or nilpotent-by-{c}hernikov‎. ‎emph{centr‎. ‎eur‎. ‎j‎. ‎math.} (to appear)] ‎‎‎of groups $g$ in w...

in which GiCG and Gi+1/Gi ⊂ Z(G/Gi) for all i. We call G solvable if it admits a normal series (1.1) in which Gi+1/Gi is abelian for all i. Every nilpotent group is solvable. Nilpotent groups include finite p-groups, and some theorems about p-groups extend to nilpotent groups (e.g., any nontrivial normal subgroup of a nilpotent group has a nontrivial intersection with the center). There is a la...