How can I prove a given abelian group; such as $\mathbb{Z}_4$ with addition mod 4, is not a free group?
Should I consider all the subsets of the given group and prove any of them cannot be a basis? But this approach will give me a lot of sub groups to consider. Is there any way to prove that multi-element subset of a group cannot be a basis, if all the elements in the subset individually cannot be a basis of the group?