In a symmetric group, a transposition is a permutation which has the effect of swapping two elements while leaving everything else unchanged. More formally, it is a permutation of order which fixes all but two elements.

A transposition is precisely an element with cycle type $2$ .

Example

In $S_{5}$ , the permutation $(12)$ is a transposition: it swaps $1$ and $2$ while leaving all three of the elements $3, 4, 5$ unchanged. However, the permutation $(124)$ is not a transposition, because it has order $3$ , not order $2$ .