In mathematics, a permutation group is a group "G" whose elements are permutations of a given set "M" and whose group operation is the composition of permutations in "G" (which are thought of as bijective functions from the set "M" to itself). The group of "all" permutations of a set "M" is the symmetric group of "M", often written as Sym("M"). The term "permutation group" thus means a subgroup of the symmetric group. If then, Sym("M"), the "symmetric group on n letters" is usually denoted by S"n".