[SOLVED] free abelian group 1. The problem statement, all variables and given/known data Show by example that is is possible for a proper subgroup of a free abelian group of finite rank r also to have rank r. 2. Relevant equations 3. The attempt at a solution I believe that there are no example in the set of finitely-generated free abelian groups. Is that right? EDIT: I think this is wrong. 2Z is a proper subgroup of Z but they both have the same rank, don't they? Is this an example in the set of infinitely-generated free abelian groups: G = Z_1 cross Z_2 cross ... H = Z_2 cross Z_4 cross ... ?