Variety of semisymmetry-like medial quasigroups and its subvarieties.

Authors

  • O.O. Tarkovska Khmelnitskiy National University

Keywords:

quasigroup, identity, parastrophe, symmetry, qroup isotope, variety, medial, asymmetric, middle symmetric, semisymmetric, totally symmetric

Abstract

In this paper, the identities defining the varieties ₰, ₰1, ₰2, which are similar to the variety of semisymmetric group isotopes are described. The conditions of coinciding quasigroups from ₰ , ₰1and ₰2and semisymmetric isotopes of a commutative group are established. According to symmetry concept, these three varieties and their parastrophic varieties, the quasigroups belonging to all these varieties are described. The relationships among all these varieties are shown.

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Issue

No. 1/2 (2015)

Section

Mathematics