Symmetric group

The symmetric group is a mathematical concept that includes all possible ways to rearrange a set of objects. For example, if you have three items—say, A, B, and C—the symmetric group includes every possible order they can be in, such as ABC, ACB, BAC, BCA, CAB, and CBA. Each of these arrangements is called a permutation. The symmetric group formalizes how these permutations combine and interact, providing a foundational framework for understanding symmetry, permutations, and group theory in mathematics.