Lattices of dominions of universal algebras

Dominions in Solvable Groups

“…Interest in research on dominions is primarily conditioned by their being densely linked with free constructions in quasivarieties of universal algebras and with amalgams (see [1] and bibliography in [2]). …”

Absolutely closed groups in the class of 2-step nilpotent torsion-free groups

“…There is a close relationship between the notions of dominion and of amalgamated free product [2]- [4]; namely,…”

Dominions in quasivarieties of metabelian groups

“…The expediency of studying dominions in quasivarieties is justified in [5] by the fact that according to [6], among axiomatizable classes, only quasivarieties possess a complete theory of defining relations, which enables us to define the free product with amalgamated subalgebra. Note that dominions were considered in detail in quasivarieties of abelian groups [3,7], and lattices of dominions were introduced and studied in [5,8,9].…”