On verbal subgroups of finitely generated nilpotent groups

Abstract

The paper concerns the problem of characterization of  verbal subgroups in finitely generated nilpotent groups. We introduce the notion of verbal poverty and show that every verbally poor finitely generated nilpotent group is a finite \(p\)-group with the lower \(p\)-central series for certain prime \(p\). We conclude with few examples of verbally poor groups.