Journal of Mathematical Sciences

, Volume 193, Issue 4, pp 639–644 | Cite as

On isotopies, parastrophies, and orthogonality of quasigroups

  • K. K. Shchukin


In V. D. Belousov’s papers, some properties of parastrophies were studied and some relations between parastrophies of a given quasigroup were obtained. Also some invariants of a parastrophy were found. This article continues our paper with V. V. Gushan, in which minimal sets of parastrophy systems for quasigroups of order 6 were obtained and some questions about orthogonality of parastrophies of a given quasigroup were studied as well.


Cyclic Group Symmetric Group Editorial Board Multiplication Table Left Translation 
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    V. D. Belousov, Parastrophy-Orthogonality Quasigroup [in Russian], Inst. Mat. AN Mold. SSR, Kishinev (1963).Google Scholar
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    V. D. Belousov, “On a group associated with a quasigroup,” Mat. Issled., 4, No. 3, 27–39 (1969).MathSciNetGoogle Scholar
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    V. D. Belousov, Elements of Quasigroup Theory [in Russian], Kishinev (1981).Google Scholar
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    K. K. Shchukin, “On isotopy, parastrophy and orthogonality of quasigroups,” Bul. Acad. Şti. Rep. Moldova, Mat., No. 3, 29–34 (2010).Google Scholar
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    K. K. Shchukin and V. V. Gushan, “Representation of parastrophies of loops and quasigroups,” Diskret. Mat., 16, No. 4, 149–157 (2004).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • K. K. Shchukin
    • 1
  1. 1.State Univeristy of MoldovaChisinauMoldova

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