Purity and Self-Small Groups

Abstract

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 , the class of self-small mixed groups G with G/tG≅ ℚ ⁿ for some n < ω. We obtain a new characterization of the elements of , and demonstrate that  differs in various ways from the class  ℱ of torsion-free abelian groups of finite rank despite the fact that the quasi-category ℚ  is dual to a full subcategory of ℚ  ℱ.

Key Words:

• Endomorphism ring
• Mixed Abelian groups
• Pure subgroups

2000 Mathematics Subject Classification:

• 20K30 (20K21; 20K25)

Notes

Communicated by K. M. Rangaswamy.