let f=(x_1, x_2,...,x_r) belongs to permutation S_n. show that order of f =r.

How to prove it?

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- Mar 19th 2008, 06:52 PMhzhang610order of permutation
let f=(x_1, x_2,...,x_r) belongs to permutation S_n. show that order of f =r.

How to prove it? - Mar 19th 2008, 06:55 PMThePerfectHacker
The thing here is to note that if you compose , times then returns back to its own position. And this happens to be the smallest such number. Thus, thus canceling both sides we get .

- Mar 19th 2008, 07:41 PMhzhang610thanks
You make it looks so easy