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Suppose G is a group of order pq such p and q are primes, p<q and...

Suppose G is a group of order pq such p and q are primes, p<q and therefore |H|=p and |K|= q, where H and K are proper subgroups are G. It was determined that H and K are abelian and G=HK. Show that H and K are normal subgroups of G without using Sylow's Theorem.

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