Dominions in varieties of nilpotent groups

Abstract

We investigate the concept of dominion (in the sense of Isbell) in several varieties of nilpotent groups. We obtain a full description of dominions in the variety of nilpotent groups of class at most two. Then we look at the behavior of dominions of subgroups of groups in \({\cal N}_2\) when taken in the context of \({\cal N}_c\) with \(c>2\). Finally we establish the existence of nontrivial dominions in the category of all nilpotent groups.