proof of class equation theorem
is a finite disjoint union of finite orbits:. We can separate this union by considerating first only the orbits of 1 element and then the rest:Then using the orbit-stabilizer theorem, we have where for every , , 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 stabilizers
are not . This finishes the proof.