Externally compatible Abelian groups of the type (2,1,0)

Abstract

In [4] the lattice of all subvarieties of the variety GnEx defined by so called externally compatible identities of Abelian groups together with the identity xn ≈ yn , for any n ∈ N and n ≥ 1 was described. In that paper classes of models of the type (2,1) where considered. It appears that diagrams of lattices of subvariaties defined by externally compatible identities satisfied in a given equational theory depend on the language of the considered class of algebras.A question was asked to what extent the diagram of the lattice of subvarieties of the variety defined by externally compatible identities of a given variety will depend on changing the type of algebras. In general case, the answer to this question seems to be very complicated. In this paper we describe the variety of Abelian groups of exponent p·q, where p,q are different primes of type (2,1,0).