English

Dominions in varieties of nilpotent groups

Group Theory 2007-05-23 v2

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 N2{\cal N}_2 when taken in the context of Nc{\cal N}_c with c>2c>2. Finally we establish the existence of nontrivial dominions in the category of all nilpotent groups.

Keywords

Cite

@article{arxiv.math/9804072,
  title  = {Dominions in varieties of nilpotent groups},
  author = {Arturo Magidin},
  journal= {arXiv preprint arXiv:math/9804072},
  year   = {2007}
}

Comments

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