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≥5, n≠6, 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. https://geodesic-test.mathdoc.fr/item/BASM_2012_1_a2/

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