If the Galois group $G$ of a polynomial of degree $n$ is 3-transitive, what can we conclude from this? Is $G=S_n$, where $S_n$ is the symmetric group of order $n$
Any Hint is useful. Thanks
[relocated the following comments by the OP here, JL]
I was reading Topics in Galois Theory by Serre. In theorem 4.4.3., says Let G be a transitive subgroup of $S_n$, which contains transposition. Then TFAE. 1)$ G$ contains $(n-1)$ cycle, 2)$G$ is doubly transitive 3) $G=S_n$.
So was wondering does any such result exist for triple transitive?