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 ${\mathcal{N}}_2$ when taken in the context of ${\mathcal{N}}_c$ with $c>2$. Finally we establish the existence of nontrivial dominions in the category of all nilpotent groups.

30 pages, plain TeX. Added results on metabelian groups, corrected typos. Final version

References in corpus (1)

• Dominions in the variety of metabelian groups

Cited by in corpus (2)

• A generalized argument for dominions in varieties of groups
• Words and Dominions