proof of class equation theorem

X is a finite disjoint unionMathworldPlanetmathPlanetmath of finite orbits: X=iGxi. We can separate this union by considerating first only the orbits of 1 element and then the rest: X=j=1l{xij}k=1sGxik=GXk=1sGxik Then using the orbit-stabilizer theorem, we have #X=#GX+k=1s[G:Gxik] where for every k, [G:Gxik]2, because if one of them were 1, then it would be associated to an orbit of 1 element, but we counted those orbits first. Then this stabilizersMathworldPlanetmath are not G. This finishes the proof.

Title proof of class equation theorem
Canonical name ProofOfClassEquationTheorem
Date of creation 2013-03-22 14:20:52
Last modified on 2013-03-22 14:20:52
Owner gumau (3545)
Last modified by gumau (3545)
Numerical id 4
Author gumau (3545)
Entry type Proof
Classification msc 20D20