Groups with non-central dimension quotients Original Research Article

Let G be a group and let Dn(G) and γn(G) be its nth dimension and nth lower central subgroups. In an earlier paper we proved that Dn(G)/γn(G) is abelian. Here we prove that Dn(G)/γn(G) is not, in general, central in G/γn(G). In fact, for any s there exists a group G and an integer n such that Dn(G)γn(G) is not contained in the sth upper central subgroups of G/γn(G).