A symmetric group, denoted as S_n, is a mathematical concept that represents the set of all possible permutations of n elements. Each permutation is a rearrangement of these elements, and the group operation is the composition of these permutations. Symmetric groups are fundamental in the field of group theory, a branch of abstract algebra. The size of a symmetric group S_n is given by n! (n factorial), which is the total number of ways to arrange n distinct objects. Symmetric groups play a crucial role in various areas of mathematics, including combinatorics, geometry, and theoretical physics, as they help in understanding the symmetries of different structures.