An abelian group \( A \) is quotient divisible if \( A \) has no torsion divisible subgroups but possesses a free subgroup \( F \) of finite rank such that \( A/F \) is a torsion divisible group. Quotient divisible groups were introduced by Beaumont and Pierce in the class of torsion-free groups in 1961, and by Wickless and Fomin, in the general case in 1998. This paper deals with the abelian groups generalizing quotient divisible groups (we refer to them as generalized quotient divisible groups or \( gqd \)-groups). We prove that an abelian group \( A \) of infinite rank is a \( gqd \)-group if and only if every \( p \)-rank of \( A \) does not exceed the rank of \( A \).

一个阿贝尔群\( A \)是商可整除的，如果\( A \)没有扭转可分子群但拥有一个有限秩的自由子群 \( F \)使得 \( A/F \)是一个扭转可分群。商可分群由 Beaumont 和 Pierce 于 1961 年在无扭群类中引入，Wickless 和 Fomin 在 1998 年在一般情况下引入。 本文讨论了推广商可分群的阿贝尔群（我们称它们为广义商可分群或\( gqd \) -groups）。我们证明了一个无穷秩的阿贝尔群 \( A \)是一个 \( gqd \) -group 当且仅当每个\( p \) -rank \( A \)不超过\( A \)的等级 。