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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- Mar 1st 2008, 07:45 PMherculesCyclic 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. - Mar 1st 2008, 07:47 PMThePerfectHacker
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.