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单词 ProofOfClassEquationTheorem
释义

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=1sGxikThen 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.

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