Let $S_n$ be the group of all permutations of the set {$1, 2, \dots,n$}.
The question is whether $S_n$ is generated by a maximum of $n-2$ of its transpositions or not.
Definitions: A permutation of a set $X$, which is a bijective function $\sigma :X\to X$, is called a cycle if the action on $X$ of the subgroup generated by $\sigma$ has exactly one orbit with more than a single element.
A cycle with only two elements is called a transposition.