# Definition:Quasigroup/Right Quasigroup

(Redirected from Definition:Right Quasigroup)

## Definition

Let $\struct {S, \circ}$ be a magma.

$\struct {S, \circ}$ is a right quasigroup if and only if:

for all $a \in S$, the right regular representation $\rho_a$ is a permutation on $S$.

That is:

$\forall a, b \in S: \exists ! x \in S: x \circ a = b$

## Also see

• Results about quasigroups can be found here.