Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 31-34
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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/
@article{FPM_2012_17_8_a4,
author = {S. Ya. Grinshpon},
title = {On a~problem related to homomorphism groups in the theory of {Abelian} groups},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {31--34},
year = {2012},
volume = {17},
number = {8},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_8_a4/}
}
TY - JOUR
AU - S. Ya. Grinshpon
TI - On a problem related to homomorphism groups in the theory of Abelian groups
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 2012
SP - 31
EP - 34
VL - 17
IS - 8
UR - http://geodesic.mathdoc.fr/item/FPM_2012_17_8_a4/
LA - ru
ID - FPM_2012_17_8_a4
ER -
%0 Journal Article
%A S. Ya. Grinshpon
%T On a problem related to homomorphism groups in the theory of Abelian groups
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2012
%P 31-34
%V 17
%N 8
%U http://geodesic.mathdoc.fr/item/FPM_2012_17_8_a4/
%G ru
%F FPM_2012_17_8_a4
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.
