Purity and self-small groups

摘要

Let A be an abelian group. A group B is A-solvable if the natural map Hom (A, B). circle times(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 congruent to Q(n) for some n < omega. 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 Q G is dual to a full subcategory of QTF.