For every nonempty set $\displaystyle A$, the algebraic structure $\displaystyle (S_A, \circ)$ is a permutation group.

The group $\displaystyle (S_A, \circ)$ is called the symmetric group on $\displaystyle A$. Therefore, every symmetric group is a permutation group.

Question:

I know a permutation is a group of functions. What makes a group symmetric? Could some one please show me an example?