Cayley's theorem
In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group "G" is isomorphic to a subgroup of the symmetric group acting on "G". This can be understood as an example of the group action of "G" on the elements of "G". The theorem can be obtained by explicitly constructing the representation within the representation of the symmetric group of permutation matrices, which is sometimes known as the regular representation.