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Abstract <p>The paper studies the properties of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--RusMath2670016Shchuchkin-m1--> </InlineEquation>-ary Т-quasigroups (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n \geqslant 3\)</EquationSource> <!--RusMath2670016Shchuchkin-m2--> </InlineEquation>). The isomorphism of the derived <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--RusMath2670016Shchuchkin-m3--> </InlineEquation>-ary groups from two Т-groups for an <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--RusMath2670016Shchuchkin-m4--> </InlineEquation>-ary Т-quasigroup is proved. A necessary and sufficient condition is found under which an <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--RusMath2670016Shchuchkin-m5--> </InlineEquation>-ary loop is a derivative of an <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--RusMath2670016Shchuchkin-m6--> </InlineEquation>-ary group from a Т-group for an <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--RusMath2670016Shchuchkin-m7--> </InlineEquation>-ary Т-quasigroup. The coincidence of the class of <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--RusMath2670016Shchuchkin-m8--> </InlineEquation>-ary T-quasigroups with the class of affine <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--RusMath2670016Shchuchkin-m9--> </InlineEquation>-ary quasigroups is proved. The heredity, homomorphic and multiplicative closure of the class of all <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--RusMath2670016Shchuchkin-m10--> </InlineEquation>-ary T-quasigroups are established, which means that this class is a variety.</p>

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Polyadic Т-Quasigroups

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • N. A. Shchuchkin

摘要

Abstract

The paper studies the properties of \(n\) -ary Т-quasigroups ( \(n \geqslant 3\) ). The isomorphism of the derived \(n\) -ary groups from two Т-groups for an \(n\) -ary Т-quasigroup is proved. A necessary and sufficient condition is found under which an \(n\) -ary loop is a derivative of an \(n\) -ary group from a Т-group for an \(n\) -ary Т-quasigroup. The coincidence of the class of \(n\) -ary T-quasigroups with the class of affine \(n\) -ary quasigroups is proved. The heredity, homomorphic and multiplicative closure of the class of all \(n\) -ary T-quasigroups are established, which means that this class is a variety.