Some Results on Baer's Theorem

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+۱(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+۱(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

Keywords:

Theorem , Lower central series , Upper central series