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