considering the core of an arbitrary group . In general if  is a group and  is a subgroup with , then  is isomorphic to a subgroup of . In particular if  is a finite group and we set  then we get the classic result.

See also 
 Wagner-Preston theorem is the analogue for inverse semigroups.
 Containment order, a similar result in order theory
 Frucht's theorem, every finite group is the automorphism group of a graph
 Yoneda lemma, an analogue of Cayley's theorem in category theory
 Representation theorem

Notes

References 
 .

Category:Permutations
Category:Theorems in group theory
Category:Articles containing proofsThe human spine serves many functions. The vertebral members of the spinal column protect the spinal cord. The spinal column also supports other portions of the human body. Furthermore, moveable facet joints and resilient discs disposed between the vertebral members permit motion between individual vertebral members. Each vertebrae includes an anterior body and a posterior arch. The posterior arch includes two pedicles and two laminae that join together to form the spinous process. A transverse process is laterally positioned at the transition from the pedicles to the laminae. Both the spinous process and transverse process provide for attachment of fibrous tissue, including muscle. Two inferior articular processes extend downward from the junction of the laminae and the transverse process. Further, two superior articular processes extend upward from the