symmetric group (original) (raw)

The group Sym⁢({1,2,…,n}) is often denoted Sn or 𝔖n.

Sn is generated by the transpositions {(1,2),(2,3),…,(n-1,n)}, and by any pair of a 2-cycle and n-cycle.

Sn is the Weyl group of the An-1 root system (and hence of the special linear group S⁢Ln-1).