Group of Permutations is Group

Theorem
Let $S$ be a set.

Let $\Gamma \left({S}\right)$ denote the set of all permutations on $S$.

Then the group of permutations on $S$ $\left({\Gamma \left({S}\right), \circ}\right)$ forms a group.

Also see

 * Group of Permutations is Subgroup of Monoid of Self-Maps