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## Main Question or Discussion Point

The problem is to verify that {(1), (1 2), (3 4), (1 2)(3 4)} is an Abelian, noncyclic subgroup of S

I was able to show that it is Abelian through pairing the permutations, but my mind stopped at the noncyclic part. When showing that a group is cyclic or noncyclic, what exactly do I have to show?

_{4}.I was able to show that it is Abelian through pairing the permutations, but my mind stopped at the noncyclic part. When showing that a group is cyclic or noncyclic, what exactly do I have to show?