User:Dfeuer/Cone Condition Equivalent to Symmetry
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Theorem
Let $(G,\circ)$ be a group with identity $e$.
Let $C$ be a cone compatible with $\circ$.
Let $\mathcal R$ be the compatible relation on $G$ induced by $C$.
Then the following are equivalent:
- $\mathcal R$ is symmetric.
- $C = C^{-1}$