Authors: Krapež, Aleksandar 
Shcherbacov, Victor
Title: Quasigroups, units and Belousov’s problem # 18
Journal: Armenian Journal of Mathematics
Volume: 11
Issue: 9
Issue Date: 1-Jan-2019
ISSN: 1829-1163
URL: http://www.armjmath.sci.am/index.php/ajm/article/view/210/150
Abstract: 
We investigate {left, right, middle} units of quasi- groups and families of identities which might imply their ex- istence. A prominent role is played by the newly introduced notion of derivative operation, generalizing Belousov’s notions of left/right derivative operations for quasigroups. Partial solu- tions of the Belousov’s Problem # 18 and its generalizations are obtained. Several related problems remain open.
Keywords: Derivative operation | Isotopy | Loop | Quasigroup | Unit
Publisher: Republic of Armenia National Academy of Sciences
Project: “Algebraic and combinatorial structures with applications”, project of the Serbian and Macedonian Academies of Sciences and Arts

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