Symmetric group of degree n

The symmetric group of degree n, denoted as \(S_n\), is the collection of all possible ways to rearrange n distinct objects. Think of it as the set of all permutations, where each permutation is a specific rearrangement. For example, with three items, all different ways to order them (like ABC, ACB, BAC, etc.) make up the group. The symmetry group captures the structure and relationships of these rearrangements, and studying it helps mathematicians understand symmetry and how objects can be transformed without changing their fundamental nature.