%0 Journal Article
%T Some Results on Baer's Theorem
%J Global Analysis and Discrete Mathematics
%I Damghan University
%Z 2476-5341
%A Faramarzi Salles, Asadollah
%D 2018
%\ 01/01/2018
%V 2
%N 2
%P 151-155
%! Some Results on Baer's Theorem
%K Theorem
%K Lower central series
%K Upper central series
%R 10.22128/gadm.2018.98
%X 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.
%U https://gadm.du.ac.ir/article_98_78d276aa42bed8cd3a9a1d786b9eb9de.pdf