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When is it hard to show that a quasigroup is a loop?

Anthony Donald Keedwell (2008)

Commentationes Mathematicae Universitatis Carolinae

We contrast the simple proof that a quasigroup which satisfies the Moufang identity ( x · y z ) x = x y · z x is necessarily a loop (Moufang loop) with the remarkably involved prof that a quasigroup which satisfies the Moufang identity ( x y · z ) y = x ( y · z y ) is likewise necessarily a Moufang loop and attempt to explain why the proofs are so different in complexity.

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