Dominions in decomposable varieties

Abstract

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 $\mathcal{N}$ has instances of nontrivial dominions, then for any proper subvariety $\mathcal{Q}$ of $\mathcal{G}roup$, $\mathcal{N}\mathcal{Q}$ also has instances of nontrivial dominions.

Plain TeX, 22 pp. Typos corrected. Final version

References in corpus (1)

• Dominions in the variety of metabelian groups