The bunch of varieties of inverse property quasigroups.

Authors

  • Fedir Sokhatsky Vasyl’ Stus Donetsk National University
  • Alla Lutsenko Vasyl’ Stus Donetsk National University

DOI:

https://doi.org/10.31558/1817-2237.2018.1-2.4

Keywords:

quasigroup, IP -quasigroup, parastrophic symmetry, group isotope, variety, truss, bunch

Abstract

In this article, the analysis of the fundamentals of the theory of quasigroups in view of the introduction of the parastrophic symmetry is continued. Parastrophic classes of inverse property quasigroups are considered. The concept of middle

Author Biographies

Fedir Sokhatsky, Vasyl’ Stus Donetsk National University

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

Alla Lutsenko, Vasyl’ Stus Donetsk National University

Postgraduate student of the Department of Mathematical Analysis and Differential Equations

References

Belousov V.D. Foundations of the theory of quasigroups and loops. Nauka (1967), 222 (Russian).

Sokhatsky F.M. On group isotopes I, Ukrainian Math. Journal, 47(10) (1995), 1585–1598.

Sokhatsky F.M. On group isotopes II, Ukrainian Math.J., 47(12) (1995), 1935–1948.

Sokhatsky F.M. On group isotopes III, Ukrainian Math.J., 48(2) (1996), 283–293.

Sokhatsky F.M. Parastrophic symmetry in quasigroup theory. Visnyk DonNU, A: natural Sciences. 2016. Vol.1-2. P. 70–83.

Pflugfelder H.O. Quasigroups and Loops: Introduction //Heldermann Verlag, Berlin, 1990.

Bruck R.H. Some results in the theory of quasigroups,Trans. Amer. Math. Soc., 55(1944), 19-52

Shcherbacov V.A. Elements of Quasigroup Theory and Applications // Chapman and Hall/CRC. – 2017.

Sokhatsky F., Syvakivskyj P. On linear isotopes of cyclic groups, Quasigroupsand related systems, 1n.1(1) (1994), 66–76.

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Issue

No. 1-2 (2018)

Section

Mathematics