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Answer to Question #50440 in Abstract Algebra for Biqilaa Silashii

Question #50440
how many associative binary operation does set with 3 elements have?
1
Expert's answer
2015-03-02T09:21:49-0500
From the article “Associative Operations on a Three-Element Set”[https://www.math.umt.edu/tmme/vol5no2and3/TMME_vol5nos2and3_a8_pp.257_268.pdf] among the 19,683 different operations on a three-element set, S = {a,b,c}, there are exactly 113 operations which are associative, in other words there exist exactly 113 three-element semigroups.

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