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SM ISO690:2012 POPOVICI, Tatiana. On conjugate sets of quasigroups
. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2011, nr. 3(67), pp. 69-76. ISSN 1024-7696. |
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
Numărul 3(67) / 2011 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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Pag. 69-76 | ||||||
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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 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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Cuvinte-cheie quasigroup, conjugate, parastrophe, identity., T -quasigroup |
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