Rank of the quotient of an Abelian group by its torsion part?

Question

Let $G$ be an Abelian group, and let $G_T$ be the torsion part of $G$. Then my question is, does the rank of $G$ always equal the rank of the quotient group $\frac{G}{G_T}$? Or can they differ in rank?

If they’re not equal in general, are there special cases that guarantee them to be equal?

Answer 1

Yes, it is the same. I found the answer in this Wikipedia article:

The set of all torsion elements is a subgroup, called the torsion subgroup and denoted T(A). A group is called torsion-free if it has no non-trivial torsion elements. The factor-group A/T(A) is the unique maximal torsion-free quotient of A and its rank coincides with the rank of A.