Thread: 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.

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.

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