Abstract
Let C be an Abelian group. A class X of Abelian groups is called a CE• H-class if for any groups A, B ∈ X, it follows from the existence of isomorphisms E• (A) ≅ E• (B) and Hom(C,A) ≅ Hom(C,B) that there is an isomorphism A ≅ B. In this paper, conditions are studied under which the class \( {\mathfrak{I}}_{\mathrm{cd}}^{\mathrm{ad}} \) of completely decomposable almost divisible Abelian groups and class \( {\mathfrak{I}}_{\mathrm{cd}}^{\ast } \) of completely decomposable torsion-free Abelian groups A where Ω(A) contains only incomparable types are CE• H-classes, where C is a completely decomposable torsion-free Abelian group.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 5, pp. 145–152, 2019.
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Pushkova, T.A. Definability of Completely Decomposable Torsion-Free Abelian Groups by Semigroups of Endomorphisms and Groups of Homomorphisms. J Math Sci 259, 484–489 (2021). https://doi.org/10.1007/s10958-021-05639-1
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DOI: https://doi.org/10.1007/s10958-021-05639-1