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 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 2012, Volume 17, Issue 8, Pages 31–34 (Mi fpm1468)

On a problem related to homomorphism groups in the theory of Abelian groups

S. Ya. Grinshpon

Tomsk State University

Abstract: 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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English version:
Journal of Mathematical Sciences (New York), 2014, 197:5, 602–604

UDC: 512.541

Citation: S. Ya. Grinshpon, “On a problem related to homomorphism groups in the theory of Abelian groups”, Fundam. Prikl. Mat., 17:8 (2012), 31–34; J. Math. Sci., 197:5 (2014), 602–604

Citation in format AMSBIB
\Bibitem{Gri12} \by S.~Ya.~Grinshpon \paper On a~problem related to homomorphism groups in the theory of Abelian groups \jour Fundam. Prikl. Mat. \yr 2012 \vol 17 \issue 8 \pages 31--34 \mathnet{http://mi.mathnet.ru/fpm1468} \transl \jour J. Math. Sci. \yr 2014 \vol 197 \issue 5 \pages 602--604 \crossref{https://doi.org/10.1007/s10958-014-1741-2} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84893844333}