Dominions in varieties of nilpotent groups

Details Dominions in varieties of nilpotent groups Dominions in varieties of nilpotent groups

1998-04-14

arxiv.org/abs/math/9804072v2

Comm. Alg. 28(3) pp. 1241-1270 (2000)

Mathematics

Group Theory

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

Scientific paper

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.

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