There’s a harder question lurking behind this question that was just asked. The context is quasigroup theory. A commutative quasigroup can be defined as a set $Q$ together with commutative binary operation $*$ such that for all $a,b \in Q$, there is a unique “solution” $s \in Q$ solving $s*a=b$. We write $b/a$ for the […]

I’m wondering, which is the smallest quasigroup which is not a group? And how to check it?

Recall that a quasigroup is a pair $(Q, \ast)$, where $Q$ is a set and $\ast$ is a binary product $$\ast: Q \times Q \to Q$$ satisfying the Latin square property, namely that for all $x, y \in Q$ there is a unique $a \in Q$ such that $y = ax$ and a unique $b […]

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