On a class of commutative groupoids determined by their associativity triples
Drápal, Aleš
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 199-201 / Harvested from Czech Digital Mathematics Library
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Let $G = G(\cdot)$ be a commutative groupoid such that $\{(a,b,c) \in G^3$; $a\cdot bc \ne ab\cdot c\} = \{(a,b,c) \in G^3$; $a=b\ne c$ or $ a \ne b =c \}$. Then $G$ is determined uniquely up to isomorphism and if it is finite, then $\operatorname{card}(G) = 2^i$ for an integer $i\ge 0$.

Publié le : 1993-01-01
Classification:  05B15,  05E99,  20L05,  20N02 
@article{118571,
     author = {Ale\v s Dr\'apal},
     title = {On a class of commutative groupoids determined by their associativity triples},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {199-201},
     zbl = {0787.20040},
     mrnumber = {1241727},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118571}
}

Drápal, Aleš. On a class of commutative groupoids determined by their associativity triples. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 199-201. http://gdmltest.u-ga.fr/item/118571/

Drápal A.; Kepka T. Sets of associative triples, Europ. J. Combinatorics 6 (1985), 227-231. (1985) | MR 0818596

Drápal A. Groupoids with non-associative triples on the diagonal, Czech. Math. Journal 35 (1985), 555-564. (1985) | MR 0809042