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Homological Properties of Quotient Divisible Abelian Groups

Abstract An abelian group A is quotient divisible if its torsion subgroup tA is reduced, and it contains a finitely generated free subgroup F such that A/F is the direct sum of a finite and a divisible torsion group. This paper focuses on homological properties of quotient divisible groups. A group A such that tA is reduced is quotient divisible if and only if it is small with respect to the class of quotient divisible groups. Further results investigate when an A-generated torsion group is A-solvable. The last section discusses quotient divisible groups A such that ℚ ⊗ℤ E(A)/tE(A) is a quasi-Frobenius ring.