The "S" in S_4(2) stands for the Symmetric group, which is a mathematical concept used to represent the collection of all possible permutations of a set of objects.
The "4" in S_4(2) represents the number of elements in the set being considered. In this case, it means that there are four objects being permuted.
The number in parentheses in S_4(2) represents the number of elements that are being used in a specific permutation. In this case, it means that two out of the four elements are being permuted while the other two remain fixed.
S_4(2) is a specific notation that indicates a permutation being performed on a set of four elements, with two of them being permuted. S_4 and S_4(3) may represent different permutations on the same set of four elements, but with different numbers of elements being permuted.
Notations like S_4(2) are used in mathematics to represent specific operations or actions being performed on a set of elements. They help to define and describe different mathematical concepts and can be used to solve problems and prove theorems.