Let G be a group with identity element e, and let H and K be subgroups of G. Assume that (i) H and K are normal in G, (ii) HNK = {e}, (iii) G = {hk | he H and k E K}. %3| Prove that G is isomorphic to the direct product H x K. (Hint : First, prove that hkh-k-1 = e for all h E H and k e K.)

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