Question

Let n be an integer ≥2 , let τ∈Sn and let X be a nonempty subset of {1,2,....,n} Say that τ fixes X if τ(X)=X, and say that τ acts irreducibly provided the only nonempty subset of {1,2,....,n} fixed by τ is {1,2,....,n} itself. Prove τ acts irreducibly if and only if τ is an n-cycle.
Please, help

Answer 1

@Zarkon