Mathematics, Informatics, Physics: Science and Education

Electronic scientific journal

Vol. 3 No. 1 (2026)
ARTICLES

Parastrophic-orthogonal ternary medial quasigroups with 3 and 4 distinct parastrophes

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  • Iryna Fryz,
  • Yevhen Pirus
Iryna Fryz
Vasyl' Stus Donetsk National University
Bio
Yevhen Pirus
Donetsk Regional Center for Educational Quality Assessment
Bio

Published 2026-05-27

Keywords

  • ternary quasigroup,
  • group isotope,
  • medial quasigroup,
  • parastrophe,
  • (strongly) orthogonal quasigroups,
  • totally parastrophic-orthogonal (top) quasigroup
    • ...More
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Copyright (c) 2026 Ірина Фриз, Євген Пірус

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Parastrophic-orthogonal ternary medial quasigroups with 3 and 4 distinct parastrophes. (2026). Mathematics, Informatics, Physics: Science and Education, 3(1), 78–90. https://doi.org/10.31652/3041-1955-2026-03-01-07
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Abstract

In the article, we study parastrophic-orthogonal ternary quasigroups: namely, group isotopes which have 3 and 4 distinct parastrophes. The necessary and sufficient conditions for ternary medial quasigroups with 3 and 4 distinct parastrophes to be totally parastrophic-orthogonal are proved. The conditions under which these quasigroups are strongly parastrophic-orthogonal are described. Thus, some methods of constructing orthogonal and strongly orthogonal ternary quasigroups are obtained.

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References

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