Geodesic
On a~problem related to homomorphism groups in the theory of Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 31-34.

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In this paper, for any reduced Abelian group $A$ whose torsion-free rank is infinite, we construct a countable set $\mathfrak A(A)$ of Abelian groups connected with the group $A$ in a definite way and such that for any two different groups $B$ and $C$ from the set $\mathfrak A(A)$ the groups $B$ and $C$ are isomorphic but $\operatorname{Hom}(B, X)\cong\operatorname{Hom}(C, X)$ for any Abelian group $X$. The construction of such a set of Abelian groups is closely connected with Problem 34 from L. Fuchs' book “Infinite Abelian Groups”, Vol. 1. 
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S. Ya. Grinshpon. On a~problem related to homomorphism groups in the theory of Abelian groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 31-34. http://geodesic.mathdoc.fr/item/FPM_2012_17_8_a4/

[1] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974

[2] Hill P., “Two problems of Fuchs concerning tor and hom”, J. Algebra, 19 (1971), 379–383 | DOI | MR | Zbl