The main concern of this paper are quasigroups of order nine that possess at most 18 associative triples. The order nine is the least order for which there exists a quasigroup Q ( , )
We show that, with finitely many exceptions, there exists a maximally nonassociative quasigroup of order n whenever n is not of the form n = 2p 1 or n = 2p 1 p 2 for primes p 1 , p 2 with p 1 p 2 < 2p 1 .
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