A generalization of co-Hopfian abelian groups

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.

n-Hopfian and n-co-Hopfian Groups

“…The leitmotif of the present article is to explore in all details the two new notions of n-Hopficity and n-co-Hopficity and to compare the obtained results with these principally known for Hopfian and co-Hopfian groups, respectively, by giving up their discrepancies. It is worthwhile noticing that some common generalizations to both Hopficity and co-Hopficity are presented in [2] and [3], respectively.…”