Definition:Symmetric Group

Theorem
The Symmetric Group of Order $$n\,$$ is denoted $$S_n\,$$ and is isomorphic to the group of all permutations of the $$n\,$$ elements of $$\mathbb {N}_n\,$$, that is, $$\left\{ {0, 1, 2, \ldots, n-1}\right\}$$.