Title of article :
Some Results on Baer’s Theorem
Author/Authors :
Faramarzi Salles ، Asadollah - Damghan University
Abstract :
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 d′i(G) =(d( G /Zi(G)))i.
Keywords :
Schur’s Theorem · Lower central series · Upper central series
Journal title :
Global Analysis and Discrete Mathematics
Journal title :
Global Analysis and Discrete Mathematics