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
M = {1,2,...,
n} then,
Sym(
M), the
symmetric group on n letters is usually denoted by
Sn.