FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 8, PAGES 31-34

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

S. Ya. Grinshpon

Abstract

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In this paper, for any reduced Abelian group $A$ whose torsion-free rank
is infinite, we construct a countable set $\$\; \backslash mathfrak\; A(A)\; \$$ 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 $\$\; \backslash mathfrak\; A(A)\; \$$ the
groups $B$
and $C$ are
isomorphic but $Hom(B,X)$≅ 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.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k118/k11804h.htm

Last modified: March 23, 2013