Dominions in decomposable varieties

Details Dominions in decomposable varieties Dominions in decomposable varieties

1998-07-21

arxiv.org/abs/math/9807118v2

Algebra Universalis 42 (2-3), 217-232 (2000)

Mathematics

Group Theory

Plain TeX, 22 pp. Typos corrected. Final version

Scientific paper

Dominions, in the sense of Isbell, are investigated in the context of decomposable varieties of groups. An upper and lower bound for dominions in such a variety is given in terms of the two varietal factors, and the internal structure of the group being analyzed. Finally, the following result is established: If a variety ${\cal N}$ has instances of nontrivial dominions, then for any proper subvariety ${\cal Q}$ of ${\cal G}roup$, ${\cal NQ}$ also has instances of nontrivial dominions.

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