Cyclic Groups

Please help me with this proof.

Prove that if a group G has no subgroup other than G and {e}, then G is cyclic.

Thanks.

Quote:

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Originally Posted by hercules

Please help me with this proof.

Prove that if a group G has no subgroup other than G and {e}, then G is cyclic.

Thanks.

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If then nothing to prove. Otherwise let , , create the subgroup , note . So, what does that means? And how does that complete the proof.