Purity and Self-Small Groups.

Let A be an abelian group. A group B is A-solvable if the natural map Hom(A, B) ⊗ E(A)A → B is an isomorphism. We study pure subgroups of A-solvable groups for a self-small group A of finite torsion-free rank. Particular attention is given to the case that A is in G, the class of self-small mixed groups G with G/tG≅ n for some n < ω. We obtain a new characterization of the elements of G, and demonstrate that G differs in various ways from the class TF of torsion-free abelian groups of finite rank despite the fact that the quasi-category G is dual to a full subcategory of TF. [ABSTRACT FROM AUTHOR]