- #1

- 22

- 0

## Homework Statement

The question is to show that the for symmetric groups, Sn with n>=3, the only permutation that is commutative is the identity permutation.

## Homework Equations

I didn't know if it was necessary but this equates to saying the center is the trivial group.

## The Attempt at a Solution

I was attempting to show that there will always exist a permutation that isn't commutative for a particular one, which I was figuring would be showing there can be permutations that move an element to different places so their compositions would be different.