Abstract

We propose a construction that allows generating large families of Latin squares, i.e., Cayley tables of finite quasigroups. This construction generalizes proper families of functions over Abelian groups introduced by Nosov and Pankratiev. We also show that all quasigroups generated by the original construction contain at least one subquasigroup, while the generalized construction generates quasigroups free of subquasigroups.

中文翻译：

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准群上的拉丁方

摘要

我们提出了一种结构，该结构可以生成较大的拉丁方族，即有限拟群的Cayley表。这种构造概括了Nosov和Pankratiev引入的Abelian群体的适当功能族。我们还表明，由原始构造生成的所有拟群都包含至少一个子拟群，而广义构造生成的子群不包含子拟群。