Generating Symmetric Group with Transpositions

56 Views Asked by At

There is a theorem in our book which I'm trying to prove, It says:

Theorem: Number of Transpositions which generate $\mathbb{S}n$ can not be lower than $n-1$.

I've already proved that $\mathbb{S}n$ can be generated by $n-1$ Transpositions, but I don't have any Idea about to show it can not be lower than that.