# Is this deduction valid for a abelian group G and dG?

We know that, any abelian group G can be written as a direct sum of dG and a reduced subgroup R (where dG is the subgroup generated by all divisible subgroups of G). Is it true that R is isomorphic to G/dG?

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Yes, it is true. –  Joel Cohen May 7 '11 at 14:40