Geodesic
Conjugate sets of loops and quasigroups. DC-quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2012), pp. 21-31

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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 investigate loops, $IP$-quasigroups and $T$-quasigroups with distinct conjugate sets described earlier. We study in more detail the quasigroups all conjugates of which are pairwise distinct (shortly, $DC$-quasigroups). The criterion of a $DC$-quasigroup (a $DC$-$IP$-quasigroup, a $DC$-$T$-quasigroup) is given, the existence of $DC$-$T$-quasigroups for any order $n\geq5$, $n\neq6$, is proved and some examples of $DC$-quasigroups are given. 
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G. B. Belyavskaya; T. V. Popovich. Conjugate sets of loops and quasigroups. DC-quasigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2012), pp. 21-31. http://geodesic.mathdoc.fr/item/BASM_2012_1_a2/