# Symmetric Group

A symmetric group is a group of all permutations of a given set.

Symmetric group is a college-level concept that would be first encountered in an abstract algebra course covering group theory.

### Prerequisites

Group: | A mathematical group is a set of elements and a binary operation that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property. |

Permutation: | In combinatorics, a permutation is a rearrangement of the elements in an ordered list S into a one-to-one correspondence with S itself. Combinatorics studies the number of possible ways of doing this under various conditions. |