# Reference Request: Subgroup of free abelian group is free abelian

I have the following reference Question, meaning that I search for a reference for the following statement: Let $F$ be a free abelian group of finite rank and $U$ be a subgroup. Then there is a basis $\{b_1, \dots, b_n\}$ of $F$ and numbers $k_1, \dots, k_l \geq 1$ $(l \leq n)$ such that $\{k_1b_1, \dots, k_lb_l\}$ is a basis of $U$.

I found a proof in Langs Algebra book that subgroups of free abelian groups are free abelian, but not this specific computation of the basis.

Thanks for any help.