Geodesic
On conjugate sets of quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2011), pp. 69-76 
Tatiana Popovich. On conjugate sets of quasigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2011), pp. 69-76. http://geodesic.mathdoc.fr/item/BASM_2011_3_a5/
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     title = {On conjugate sets of quasigroups},
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     year = {2011},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2011_3_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is known that the set of conjugates (the conjugate set) of a binary quasigroup can contain 1, 2, 3 or 6 elements. We establish a connection between different pairs of conjugates and describe all six possible conjugate sets, with regard to the equality (“assembling”) of conjugates. Four identities which correspond to the equality of a quasigroup to its conjugates are pointed out. Every conjugate set is characterized with the help of these identities. The conditions of the equality of a $T$-quasigroup to conjugates are established and some examples of $T$-quasigroups with distinct conjugate sets are given.

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