Geodesic
On conjugate sets of quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2011), pp. 69-76

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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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     author = {Tatiana Popovich},
     title = {On conjugate sets of quasigroups},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {69--76},
     publisher = {mathdoc},
     number = {3},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2011_3_a5/}
}
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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/