class equation theorem

Let G be a group acting on a finite setMathworldPlanetmath X. Define the set of invariants in X by the action of G as GX={xX|gx=xgG}. Then there are H1,,Hr subgroupsMathworldPlanetmathPlanetmath of G with HiGi such that #X=#GX+i=1r[G:Hi]

Title class equation theorem
Canonical name ClassEquationTheorem
Date of creation 2013-03-22 14:20:50
Last modified on 2013-03-22 14:20:50
Owner gumau (3545)
Last modified by gumau (3545)
Numerical id 5
Author gumau (3545)
Entry type Theorem
Classification msc 20D20
Synonym class equation
Related topic CentralizerMathworldPlanetmathPlanetmathPlanetmath