stabilizer (original) (raw)

Let G be a group, X a set, and ⋅:G×X⟶X a group action . For any subset S of X, the stabilizer of S, denoted Stab⁡(S), is the subgroup

Stab⁡(S):={g∈G∣g⋅s∈S⁢for all ⁢s∈S}.

The stabilizer of a single point x in X is often denoted Gx.