TAMENESS OF THE PSEUDOVARIETY OF ABELIAN GROUPS
Jorge Almeida, Manuel Delgado · International Journal of Algebra and Computation · 2005
In this paper we prove that the pseudovariety of Abelian groups is hyperdecidable and moreover that it is completely tame. This is a consequence of the fact that a system of group equations on a free Abelian group with certain rational constraints is solvable if and only if it is solvable in every finite quotient.