Abstract
Recently, a great deal of attention has been paid to the concept of quasipure injectivity introduced by L. Fuchs as Problem 17 in [5]. An abelian group G is said to be quasi-pure-injective (q.p.i.) if every homomorphism from a pure subgroup of G to G can be lifted to an endomorphism of G. D. M. Arnold, B. O'Brien and J. D. Reid have succeeded in [1] to characterize torsion free q.p.i. of finite rank, whereas in [2] we solved the torsion case and in [3] we studied certain classes of infinite rank torsion free q.p.i. groups.
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