Prove: Let H be a finite group of permutations of the set Y. Suppose Y acts transitivity on Y. Then Y is a finite set, and |Y|divide |H|
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Prove: Let H be a finite group of permutations of the set Y. Suppose Y acts transitivity on Y. Then Y is a finite set, and |Y|divide |H|
It's a standard theorem thatas H-sets where
and
and since
acts transitively
so we have
and the result is immediate.