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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