I'm confused on how to find the orbits of elements.
The orbit for $\sigma\in S_X $ is defined to be $O_{x,\sigma} = \{y\,|\,\sigma^n (x) = y\}$.
I need to compute the orbit of the permutation $\alpha = (1254)$.
I think the notation $\sigma^n (x)$ is confusing me more than anything else. Would the orbit just be the set $\{\sigma \alpha,\sigma^2 \alpha, \sigma^3 \alpha\, \sigma^4 \alpha, \alpha\}$?
Why or why not?
Can someone explain this for me?