Abstract
Let \(C\) be an Abelian group. A class \(X\) is said to be a \(_{C}H\)-class if, for any groups \(A,B\in X\), a group isomorphism of \(\operatorname{Hom}(C,A)\) and \(\operatorname{Hom}(C,B)\) implies an isomorphism of the groups \(A\) and \(B\). In the paper, conditions on a completely decomposable Abelian group \(C\) are investigated under which a class of certain completely decomposable torsion-free Abelian groups is a \(_{C}H\)-class.
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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 738–741 https://doi.org/10.4213/mzm13736.
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Pushkova, T.A., Sebel’din, A.M. On the Question of the Definability of Certain Classes of Completely Decomposable Abelian Torsion-Free Groups by Their Homomorphism Groups. Math Notes 113, 700–703 (2023). https://doi.org/10.1134/S0001434623050097
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DOI: https://doi.org/10.1134/S0001434623050097