Let G be a group, X a set, and :G×XX a group actionMathworldPlanetmath. For any subset S of X, the stabilizerMathworldPlanetmath of S, denoted Stab(S), is the subgroupMathworldPlanetmathPlanetmath

Stab(S):={gGgsSfor all sS}.

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

Title stabilizer
Canonical name Stabilizer
Date of creation 2013-03-22 12:12:22
Last modified on 2013-03-22 12:12:22
Owner djao (24)
Last modified by djao (24)
Numerical id 7
Author djao (24)
Entry type Definition
Classification msc 20M30
Classification msc 16W22
Synonym isotropy subgroup