Classification of ternary quasigroups according to their parastrophic symmetry groups, I.

Authors

  • Fedir Sokhatsky Vasyl’ Stus Donetsk National University
  • Yevhen Pirus Donetsk Regional Center for Educational Quality Assessment

DOI:

https://doi.org/10.31558/1817-2237.2018.1-2.5

Keywords:

ternary quasigroup, variety of a quasigroup, parastrophic quasigroups, parastrophic symmetry, parastrophic varieties, parastrophic symmetry groups

Abstract

Quasigroups as algebraic structures are very suitable for construction of cryptographic primitives. There are several classifications of quasigroups. Most of them are made for binary quasigroups.

Author Biographies

Fedir Sokhatsky, Vasyl’ Stus Donetsk National University

Doctor in Physics and Mathematics, Professor of the Department of Mathematical Analysis and Differential Equations

Yevhen Pirus, Donetsk Regional Center for Educational Quality Assessment

head of department of information technologies

References

Sokhatsky F.M. Parastrophic symmetry in quasigroup theory. Bulletin of Donetsk National University. Series A: Natural Sciences. 2016. (1/2), 70–83.

Sokhatsky F.M. Factorization of operations of medial and abelian algebras. Bulletin of Donetsk National University. Series A: Natural Sciences. 2017.

Сохацкий Ф.Н., Кирнасовский О.Е. Канонические разложения многоместных изотопов групп. // Известия Гомельского государственного университета им. Ф.Скорины, 2001, N3(6). — Вопросы алгебры.– 17, С.88–97

Белоусов В.Д. n -арные квазигруппы //Кишинев:Штиинца.– 1972. – 222 c.

Сохацький Ф.М. Асоцiати та розклади багатомiсних операцiй. // Дисертацiя на здобуття наук.ступ.доктора фiз.—мат.наук. — Київ. — 2006.

Белоусов В.Д. Основы теории квазигрупп и луп //М.: Наука.– 1967. – 222 c.

Белоусов В.Д. Конфигурации в алгебраических сетях // Кишинев: Штиинца.— 1979.— 143 с.

Fedir M. Sokhatsky, Iryna V .Fryz, Invertibility criterion of composition of two multiary operations. Comment. Math. Univ. Carolin. 53,3(2012) 429–445.

F.M. Sokhatsky About of group isotopes I. Ukrainian Math.Journal, 47(10) (1995), 1585−−1598 .

F.M. Sokhatsky About of group isotopes II. Ukrainian Math.J., 47(12) (1995), 1935 − −1948 .

F.M. Sokhatsky About of group isotopes III. Ukrainian Math.J., 48(2) (1996), 283 − −293 .

Sokhatsky Fedir, Syvakivskyj Petro On linear isotopes of cyclic groups, Quasigroups and related systems, 1 n.1(1) (1994), 66 − 76 .

Halyna V. Krainichuk Classification of group isotopes according to their symmetry groups // Folia Math. — 2017. — Vol. 19, no. 1. — P. 84–98

Krainichuk H., Tarkovska O. Semi-symmetric isotopic closure of some group varieties and the corresponding identities // Bul. Acad. ¸Stiin¸te Repub. Mold. Mat. — 2017. — № 3(85). — P. 3–22.

Dimitrova, V., Mihajloska, H Classification of ternary quasigroups of order 4 applicable in cryptography , in print, 7 International Conference of Informatics and Information Technology, Bitola, Feb. 2010

Dimitrova Vesna, Mihajloska Hristina “An Application of Ternary Quasigroup String Transformations.” , 2010

S. Nelson and S. Pico. Virtual tribrackets. arXiv:1803.03210, 2018.

M. Niebrzydowski. On some ternary operations in knot theory . Fund. Math., 225(1):259–276, 2014.

M. Niebrzydowski. Ternarny quasigroups in knot theory arXiv: 1708.05330, 2018

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Mathematics