Abstract
We define the concept of an [Formula: see text]-co-Hopfian abelian group, which is a nontrivial generalization of the classical notion of a co-Hopfian group. A systematic and comprehensive study of these groups is given in very different ways. Specifically, a representation theorem for [Formula: see text]-co-Hopfian groups is established as well as it is shown that there exists an [Formula: see text]-co-Hopfian group which is not co-Hopfian.
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