# Math Help - Cyclic Groups

1. ## 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.

2. 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 $G=\{ e\}$ then nothing to prove. Otherwise let $a\in G$, $a\not = e$, create the subgroup $H=\left< a\right>$, note $H\not = \{ e\}$. So, what does that means? And how does that complete the proof.