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I am considering finite magmas $(S,\cdot)$ with $\forall(x,y,z)\in S^3, x\cdot(y\cdot z)=y\cdot(x\cdot z)$. Any finite commutative group is an example of such thing. But in the context (this question on crypto.stackexchange.com), I am not interested in groups; or at least, not in groups with an efficiently computable inverse.

I am wondering if/how the classical magma-to-group classification simplifies for such structures. magma to group

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    Actually, existence of identity is enough for it to imply commutativity.2012-07-08

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