Can I get help on the following problem:
Show that if n GE 3 then the center of Sn is of order 1.
Let be non-trivial permutation. Then there exists such that with . Notice that has at most three distinct points, let be different from all three of these (since this is possible). There exists a permutation which satisfies . Thus, and . We see that . This shows if is not trivial then it cannot lie in the center.