Question: prove that every subgroup of an abelian group is normal?
Answer: Prove that any subgroup of an Abelian group is normal subgroup. Answer: Recall: A subgroup H of a group G is called normal if gH = Hg for every g ∈ G. ... gh = hg for all h since G is Abelian. Therefore {gh | h ∈ H} = {hg | h ∈ H} = Hg by definition of right coset Hg.