High nonassociativity in order 8 and an associative index estimate |
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| Authors: | Ale&#x; Drpal Viliam Valent |
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| Institution: | Ale? Drápal,Viliam Valent |
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| Abstract: | Let  be a quasigroup. Put  and assume that  . Let  and  be the number of left and right translations of  that are fixed point free. Put  . Denote by  the number of idempotents of  . It is shown that  . Call  extremely nonassociative if  . The paper reports what seems to be the first known example of such a quasigroup, with  ,  , and  . It also provides supporting theory for a search that verified  for all quasigroups of order  . |
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| Keywords: | associative triple associativity index combinatorial inequality quasigroup |
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