Group is Quasigroup

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Theorem

Let $\left({G, \circ}\right)$ be a group.

Then $\left({G, \circ}\right)$ is a quasigroup.


Proof

By the definition of a quasigroup it must be shown that:

$\forall g \in G$ the left and right regular representations of $\lambda_g$ and $\rho_g$ are permutations on $G$.

This follows immediately from Regular Representations in Group are Permutations.

$\blacksquare$