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On 4-T-quasigroups with exactly 20 distinct parastrophes
Authors: Tatiana Rotari, Parascovia Syrbu
Keywords: n-quasigroup, n-T-quasigroup, T-form, parastrophe, spectrum
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Keywords: n-quasigroup, n-T-quasigroup, T-form, parastrophe, spectrum
Abstract
The $T-$forms and the spectrum of $4-T-$quasigroups with exactly $20$ distinct parastrophes are considered in the present work. Characterizations of the spectra of finite binary quasigroups with a prescribed number of distinct parastrophes were given by C.C. Lindner and D. Steedly in [1]. Following the results of C.C. Lindner and D. Steedly, M. MacLeish proved that the maximum number of distinct parastrophes of an $n-$quasigroup $(Q, A)$ is a divizor of $(n+1)!,$ and obtained characterizations of the spectrum of finite ternary quasigroups with a prescribed (maximum) number of distinct parastrophes. Binary and ternary linear quasigroups over groups, with a given maximum number of distinct parastrophes have been studied by Belyavskaya, Rotari, Sokhatsky, Pirus, Fryz and others [4-8]. Characterizations of the general $T-$form of a $4-T-$quasigroup with exactly $20$ distinct parastrophes and some estimations of their spectrum are given in the present work.Tatiana Rotari
Alecu Russo Balti State University,
Chair of Mathematics and Science
E-mail:
Parascovia Syrbu
Moldova State University,
Department of Mathematics
E-mail:
Alecu Russo Balti State University,
Chair of Mathematics and Science
E-mail:
Parascovia Syrbu
Moldova State University,
Department of Mathematics
E-mail:
DOI
https://doi.org/10.56415/basm.y2025.i1.p107Fulltext
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Contents
- Generalized Berezin transform and Schatten class operators on weighted Bergman spaces
- Reverse Hardy inequalities via μ-proportional generalized fractional integral operators
- Some integrals for cosine families of bounded linear operators on some non-Archimedean Banach spaces
- About the Laplace transform on ${{L}^{1}}\left( \mathbb{R^+} \right)$
- Vertical Generalized Berger-type Metrics: A New Perspective on Harmonic Vector Fields
- On conharmonic curvature tensor of 6-dimensional planar Hermitian submanifolds of Cayley algebra
- Completeness of the factor group of a complete topological group and completeness of the factor ring of a complete topological ring by a compact normal subgroup and a compact ideal, respectively.
- Pure and Mixed Stationary Equilibria for Dynamic Positional Games on Graphs
- On 4-T-quasigroups with exactly 20 distinct parastrophes
