Dihedral groups are ambivalent

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This article gives the statement, and possibly proof, of a particular group or type of group (namely, Dihedral group (?)) satisfying a particular group property (namely, Ambivalent group (?)).

Statement

The dihedral group D_{2n} is an ambivalent group: every element is conjugate to its inverse. Note that this also holds for the infinite dihedral group.

For finite dihedral groups, this implies that all irreducible characters (and hence, all characters) are real-valued.

Related facts