Editing Mapping class group (section)

=== Symmetry group of knot and links ===
If ''K'' ⊂ '''S'''<sup>3</sup> is a [[knot (mathematics)|knot]] or a [[link (knot theory)|link]], the '''symmetry group of the knot (resp. link)''' is defined to be the mapping class group of the pair ('''S'''<sup>3</sup>, ''K'').  The symmetry group of a [[hyperbolic knot]] is known to be [[dihedral group|dihedral]] or [[cyclic group|cyclic]]; moreover every dihedral and cyclic group can be realized as symmetry groups of knots.  The symmetry group of a [[torus knot]] is known to be of order two '''Z'''<sub>2</sub>.