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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- Nov 13th 2009, 07:58 PMapple2009permutation/transitivity
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|

- Nov 13th 2009, 08:55 PMJose27
It's a standard theorem that as H-sets where and and since acts transitively so we have and the result is immediate.