# Symmetric groups are strongly ambivalent

From Groupprops

## Statement

### For a finite set

For any natural number , the Symmetric group (?) of degree is a Strongly ambivalent group (?). In other words, every element of is a Strongly real element (?): it is either the identity element or is conjugate to its inverse via an element of order two.

### General statement

The symmetric group on any set is a strongly ambivalent group. In other words, every element of the group is a strongly real element.