Symmetric groups are strongly ambivalent

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Statement

For a finite set

For any natural number n, the Symmetric group (?) S_n of degree n is a Strongly ambivalent group (?). In other words, every element of S_n 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.

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