中三元自正交拟群的构造

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica Pub Date : 2023-06-01 DOI:10.56415/basm.y2022.i3.p41

I. Fryz, F. Sokhatsky

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摘要

给出了判别中三元拟群是否存在6个三向正交主对偶集和6个三向强正交主对偶集的算法。证明了$n$-一元强自正交线性(含中)拟群在$n$ > $ 3$时不存在。

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Construction of medial ternary self-orthogonal quasigroupsm

Algorithms for checking if a medial ternary quasigroup has a set of six triple-wise orthogonal principal parastrophes and a set of six triple-wise strongly orthogonal principal parastrophes are found. It is proved that $n$-ary strongly self-orthogonal linear (including medial) quasigroups do not exist when $n>3$.

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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

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