Definition:Ambivalent Group

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.