# Cyclic Groups

• Mar 1st 2008, 08:45 PM
hercules
Cyclic Groups

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

Thanks.
• Mar 1st 2008, 08:47 PM
ThePerfectHacker
Quote:

Originally Posted by hercules
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.