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Proving that an Abelian group of order pq is isomorphic to Z_pq
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[QUOTE="Mr Davis 97, post: 5717798, member: 515461"] [h2]Homework Statement [/h2] Given that G is an abelian group of order pq, I need to show that G is isomorphic to ##\mathbb{Z}_{pq}## [h2]Homework Equations[/h2][h2]The Attempt at a Solution[/h2] I am trying to do this by showing that G is always cyclic, and hence that isomorphism holds. If there is an element of order pq, then we immediately see that G is cyclic. If there is an element x of order p, I want to show that the there is an element y not in the cyclic subgroup generated by x, such that the order of xy is pq, which would mean that G is cyclic, right. How could I go about doing this? [/QUOTE]
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Proving that an Abelian group of order pq is isomorphic to Z_pq
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