Ambivalent group
= Ambivalent group
A finite group is ambivalent when every element is conjugate to its inverse. Since every complex character satisfies $\chi(g^{-1})=\overline{\chi(g)}$, an ambivalent group has real values for every <irreducible character>. Conversely, if every irreducible value is real, <irreducible characters separate conjugacy classes> and force every $g$ to be conjugate to $g^{-1}$.