A generalization of quotient divisible groups to the infinite rank case (Q2030782)

An abelian group \(A\) is quotient divisible if \(A\) has no torsion divisible subgroup, but \(A\) has a free subgroup \(F\) of finite rank such that \(A/F\) is torsion divisible. The author generalizes this concept to the infinite rank case by defining \(A\) to be generalized quotient divisible if \(A\) has a free subgroup \(F\) such that \(A/F\) is torsion divisible. He proves that an infinite rank abelian group \(A\) is generalized quotient divisible if and only if every \(p\)-rank of \(A\) does not exceed the rank of \(A\).