1. ## groups of permutations

Let pi is a cycle in S(n) of length r. Prove that ord(pi) = r.

2. Originally Posted by anncar
Let pi is a cycle in S(n) of length r. Prove that ord(pi) = r.
It is quite stairtforward. Let $\pi = (1,2,3)$ in $S_5$ for example. Not if you compose $\pi$ with itself 3 times each element goes to itself. This happens to be its order.

3. hi, could you explain it more thoroughly?..like- what everything means? thanks.

4. Originally Posted by anncar
hi, could you explain it more thoroughly?..like- what everything means? thanks.
TPH meant that if you take any element $\pi \in S_n$ of length r, and if you compose $\pi$ r times, that is, $\underbrace{\pi \pi ... \pi}_{r \, times}$, then you will get $(1)$, the identity.. hence, the order is r..