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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, Number 1, Pages 21–31 (Mi basm307)  

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.

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Document Type: Article
MSC: 20N05, 05B15
Received: 24.06.2011
Language: English

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

Citation in format AMSBIB
\Bibitem{BelPop12}
\by G.~B.~Belyavskaya, T.~V.~Popovich
\paper Conjugate sets of loops and quasigroups. DC-quasigroups
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2012
\issue 1
\pages 21--31
\mathnet{http://mi.mathnet.ru/basm307}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2987324}
\zmath{https://zbmath.org/?q=an:1253.20060}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. B. Belyavskaya, T. V. Popovich, “Near-totally conjugate orthogonal quasigroups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 3, 89–96  mathnet
    2. Halyna Krainichuk, Olena Tarkovska, “Semi-symmetric isotopic closure of some group varieties and the corresponding identities”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 3, 3–22  mathnet
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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