Finite-by-nilpotent groups

1. Introduction . 1·1. Notation . Let and be, respectively, the upper and lower central series of a group G . By definition, Z i +1 / Z i is the centre of G / Z i and Γ j +1 = [Γ j , G ] is the commutator subgroup of Γ j with G . When necessary for clearness, we write Z i G) for Z i and Γ j ( G ) for Γ j .