Symmetric groups are ambivalent
This article gives the statement, and possibly proof, of a particular group or type of group (namely, Symmetric group (?)) satisfying a particular group property (namely, Ambivalent group (?)).
Statement
The symmetric group on any set is an ambivalent group: every element is conjugate to its inverse.
Related facts
Stronger facts
- Symmetric groups are rational
- Symmetric groups are rational-representation
- Symmetric groups are strongly ambivalent
Related facts about alternating groups
- Classification of ambivalent alternating groups
- Classification of alternating groups having a class-inverting automorphism
- Finitary alternating group on infinite set is ambivalent