conjugacy class (original) (raw)

Let G a group, and consider its operation (action) on itself give by conjugation , that is, the mapping

(g,x)↦g⁢x⁢g-1

Since conjugation is an equivalence relation , we obtain a partition of G into equivalence classes , called conjugacy classes . So, the conjugacy class of X (represented Cx or C⁢(x) is given by

Cx={y∈X:y=g⁢x⁢g-1⁢for some ⁢g∈G}