Proceedings of the Glasgow Mathematical Association

Research Article

Remarks on the Upper Centralc Series of a Group

D. H. McLaina1

a1 The University Glasgow

Following, for example, Kurošs [8], we define the (transfinite) upper central series of a group G to be the series

S2040618500033414_eqnU1

such that Zα + 1/Za is the centre of G/Zα, and if β is a limit ordinal, then S2040618500033414_inline1 If α is the least ordinal for which Zα =Zα+1=…, then we say that the upper central series has length α, and that Zα= His the hypercentre of G. As usual, we call G nilpotent if Zn= Gfor some finite n.

(Received November 10 1955)