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International Journal of Mathematics and Mathematical Sciences
Volume 2, Issue 1, Pages 69-80

The group of homomorphisms of abelian torsion groups

Department of Mathematics, Moorhead State University, Moorhead 56560, Minnesota, USA

Received 10 February 1978

Copyright © 1979 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let G and A be abelian torsion groups. In[5], R. S. Pierce develops a complete set of invariants for Hom(G, A). To compute these invariants he introduces, and uses extensively, the group of small homomorphisms of G into A. Also, using some of Pierce's methods, Fuchs characterizes this group in [1]. Our purpose in this paper is to characterize Hom(G, A) in what seems to be a more natural manner than either of the treatments just mentioned.