Varieties of idempotent commutative groupoids
We give an equational description of all idempotent groupoids with at most three essentially n-ary term operations.
We contrast the simple proof that a quasigroup which satisfies the Moufang identity is necessarily a loop (Moufang loop) with the remarkably involved prof that a quasigroup which satisfies the Moufang identity is likewise necessarily a Moufang loop and attempt to explain why the proofs are so different in complexity.