# 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.