Let $G$ be a group generated by $a$ and $b$ such that order$(a)=2$ and order$(b)=n$. What condition can I impose to $a$ and $b$ to get $G \cong S_n$?
The group $G$ that I'm looking at is a little complicated but I think that is actually isomorphic to $S_n$, so I'm looking for a condition that can prove that.
