Thread: 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.

Originally Posted by rainyice

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