Abelian groups

Question

Is every subgroup of an abelian group abelian?

Answer 1

Yes.
Proof:- Let G be an abelian group, and suppose that H ≤ G. Now we have to check that,  for any a, b ∈ H,
we have ab = ba.
 a, b ∈ H ⊆ G
so ab = ba,
since G is abelian.
Therefore, H is abelian as well.