Permutation groups

A **permutation group** is a mathematical structure consisting of a set of permutations that can be combined in a way that satisfies the properties of a group. Specifically, if you have a set \( X \), a permutation is a bijective function that rearranges the elements of \( X \). The collection of all possible permutations of a finite set \( X \) of size \( n \) is called the symmetric group, denoted as \( S_n \).