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Math Help - Prove that any nontrivial subgroup of G is cyclic.

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    Prove that any nontrivial subgroup of G is cyclic.

    Let G be a group of order pq, where p and q are primes. Prove that any nontrivial subgroup of G is cyclic.
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    Quote Originally Posted by rainyice View Post
    Let G be a group of order pq, where p and q are primes. Prove that any nontrivial subgroup of G is cyclic.

    What are the possible orders for such a subgroup according to Lagrange's Theorem? Then what can you deduce?

    Tonio
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