Question

what is the difference s subgroup and abelian group​

Answer 1

Answer:

subgroups of abelian groups are indeed abelian, and your thought process has the right idea. Showing this is pretty easy. Take an abelian group G with subgroup H. Then we know that, for all a,b∈H, ab=ba since it must also hold in G (as a,b∈G≥H and G is given to be abelian)