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Sets of associative triples. (English) Zbl 0612.05003
Authors’ summary: ”A subset $$R\subseteq S^ 3$$ will be called (associatively) admissible if there exists a binary operation * defined on S such that $$x*(y*z)=(x*y)*z$$ iff (x,y,z)$$\in R$$. If S is finite, $$card(S)=n$$, $$R\subseteq S^ 3$$, $$card(R)=r$$ and $$r\leq n/4-3/4$$ or $$n^ 3-n/4+1/2\leq r$$, then R is admissible. There exists an admissible subset for any $$0\leq r\leq n^ 3$$ and a non-admissible subset for 3n$$\leq r\leq n^ 3-n+2.$$”
Reviewer: K.Burian

##### MSC:
 05A05 Permutations, words, matrices