Description: Cayley's Theorem (existence version): every group G is isomorphic to a subgroup of the symmetric group on the underlying set of G . (For any group G there exists an isomorphism f between G and a subgroup h of the symmetric group on the underlying set of G .) See also Theorem 3.15 in Rotman p. 42. (Contributed by Paul Chapman, 3-Mar-2008) (Revised by Mario Carneiro, 13-Jan-2015)