Some Results on Baer's Theorem


Department of Mathematics, Damghan University, Damghan, Iran.


Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(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+1(G)|d i(G), where di(G) =(d( G /Zi(G)))i.


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