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A Note on Fuch's Problem 34

U. F. Albrecht and H. P. Goeters
Proceedings of the American Mathematical Society
Vol. 124, No. 5 (May, 1996), pp. 1319-1328
Stable URL: http://www.jstor.org/stable/2161437
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Note on Fuch's Problem 34
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Abstract

We investigate to what extent an abelian group G is determined by the homomorphism groups G is determined by the homomorphism groups $\operatorname{Hom}(G, B)$ where B is chosen from a set X of abelian groups. In particular, we address Problem 34 in Professor Fuchs' book which asks if X can be chosen in such a way that the homomorphism groups determine G up to isomorphism. We show that there is a negative answer to this question. On the other hand, there is a set X which determines the torsion-free groups of finite rank up to quasi-isomorphism.

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