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 SM ISO690:2012BELEAVSCAIA, Galina, POPOVICI, Tatiana. Conjugate sets of loops and quasigroups. DC-quasigroups. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2012, nr. 1(68), pp. 21-31. ISSN 1024-7696. |
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 Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica |
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| Numărul 1(68) / 2012 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| Pag. 21-31 | ||||||
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| Rezumat | ||||||
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= 6,
is proved and some examples of DC-quasigroups are given. |
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| Cuvinte-cheie quasigroup, loop, T-quasigroup, conjugate, parastrophe, identity., IP-quasigroup |
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