Latin Squares over Quasigroups

被引：2
作者：
Galatenko, A. V. [1 ]
Nosov, V. A. [1 ]
Pankratiev, A. E. [1 ]
机构：
[1] LomonosovMoscow State Univ, Moscow 119991, Russia
来源：
LOBACHEVSKII JOURNAL OF MATHEMATICS | 2020年 / 41卷 / 02期
关键词：
quasigroup; proper family of functions; subquasigroup;
D O I：
10.1134/S1995080220020079
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：194 / 203
页数：10
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