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Dominions in varieties of nilpotent groups

Arturo Magidin
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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.

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Arturo Magidin. 1999-05-13. Dominions in varieties of nilpotent groups. https://arxiv.org/abs/math/9804072

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