Show that if H and K are subgroups of an abelian group G, then {hk|h € H and k e K} is a subgroup of G.
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- 10. Suppose that and are subgroups of the abelian group such that . If is a subgroup of such that , prove that .Let H1 and H2 be cyclic subgroups of the abelian group G, where H1H2=0. Prove that H1H2 is cyclic if and only if H1 and H2 are relatively prime.34. Suppose that and are subgroups of the group . Prove that is a subgroup of .