Symmetric groups

Given the set Sn of the permutations of the n elements of a set S, the set S_n forms a group (S_n, o) with respect to the permutation operation o.

$$ (S_n, \text{o}) $$

The group of all permutations S_n of the n symbols is called a symmetric group.

The subgroups of S_n are called permutation groups.

Note. Permutation groups and symmetric groups are non-Abelian (non-commutative) groups because the permutation operation o is non-commutative.