Nonassociative triples in involutory loops and in loops of small order
Aleš Drápal, Jan Hora (2020)
Commentationes Mathematicae Universitatis Carolinae
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A loop of order possesses at least associative triples. However, no loop of order that achieves this bound seems to be known. If the loop is involutory, then it possesses at least associative triples. Involutory loops with associative triples can be obtained by prolongation of certain maximally nonassociative quasigroups whenever is a prime greater than or equal to or , an odd prime. For orders the minimum number of associative triples is reported for both general...