Definition:Ambivalent Group
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Definition
Let $G$ be a group.
Then $G$ is ambivalent if and only if every element of $G$ is conjugate to its inverse:
- $\forall g \in G : \exists h \in G : h g h^{-1} = g^{-1}$
That is, if and only if every element of $G$ is real.
Also see
- Definition:Real Group Element
- Results about ambivalent groups can be found here.