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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2012, Number 1, Pages 21–31
(Mi basm307)
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This article is cited in 2 scientific papers (total in 2 papers)
Conjugate sets of loops and quasigroups. DC-quasigroups
G. B. Belyavskaya, T. V. Popovich Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova
Abstract:
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.
Keywords and phrases:
quasigroup, loop, $IP$-quasigroup, $T$-quasigroup, conjugate, parastrophe, identity.
Received: 24.06.2011
Citation:
G. B. Belyavskaya, T. V. Popovich, “Conjugate sets of loops and quasigroups. DC-quasigroups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 1, 21–31
Linking options:
https://www.mathnet.ru/eng/basm307 https://www.mathnet.ru/eng/basm/y2012/i1/p21
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Abstract page: | 333 | Full-text PDF : | 85 | References: | 48 | First page: | 1 |
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