Remarks on the Upper Centralc Series of a Group

Abstract

Following, for example, Kurošs [8], we define the (transfinite) upper central series of a group G to be the series such that Z α + 1 /Z a is the centre of G/Z α , and if β is a limit ordinal, then If α is the least ordinal for which Z α =Z α+1 =…, then we say that the upper central series has length α, and that Z α = H is the hypercentre of G . As usual, we call G nilpotent if Z n = G for some finite n .