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Notes on the number of associative triples. (English) Zbl 0786.20042
Some questions concerning the number of associative triples in a quasigroup are discussed. The authors divide the paper into three parts. In part 1 some definitions and examples are given. For instance, they present two examples of a quasigroup $$H$$ of order 6 with $$a(H) = 16$$ and a quasigroup $$Q$$ of order 6 with $$a(Q) = 189$$ ($$a(Q)$$ is the associative spectrum of $$n$$, for every $$n\geq 1$$, where $$Q$$ runs over the quasigroups of order $$n$$). In part 2 are given three examples, and in part 3 they discuss the group distance and the numbers $$b_{\min}(n)$$, where $$b_{\min}(n)$$ denote the minimum of the numbers $$b(Q)$$, for $$Q$$ running over all the nonassociative quasigroups of order $$n\geq 3$$.

##### MSC:
 20N05 Loops, quasigroups
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