An isomorphic refinement theorem for Abelian groups
Robert B. Warfield · Pacific Journal of Mathematics · 1970
Lemma 1 is obvious except perhaps for property (ii) for which see [4, Lemma 3.10].Lemma 2 is immediate from the finite exchange property.The groups in ^ actually have the exchange property (not just the finite exchange property).For a proof we refer to [3, Lemma 3.6], only remarking that one must use our Lemmas 6 and 7 ΐelow instead of Crawley's 3.2 and 3.3.We will not need this result.We will state our main results for abstract classes of groups, since the class c ^ is not the only class of groups for which these theorems can be proved.