the theorem asserting that the divisible subgroup of an Abelian group is a direct summand depends on Zorn's lemma.
in ZF without AC is there a construction which yields a model of an Abelian group which does not have this property?
note:my motive in asking this is less curiosity about group theory and more the hope that answers might help me begin to understand the still-elusive ideas of forcing and boolean-valued models. apologies if the question is unfit for purpose