Armenian Journal of Mathematics

Quasigroups, Units and Belousov's Problem # 18

Krapez, Aleksandar and Shcherbacov, Victor A. (2019) Quasigroups, Units and Belousov's Problem # 18. Armenian Journal of Mathematics, 11 (9). pp. 1-27. ISSN 1829-1163

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We investigate {left, right, middle} units of quasigroups and families of identities which might imply their existence. 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 solutions of the Belousov's Problem # 18 and its generalizations are obtained. Several related problems remain open.

Item Type:Article
Uncontrolled Keywords:Quasigroup, Loop, Unit, Derivative operation, Isotopy
Subjects:05-xx Combinatorics
20-xx Group theory and generalizations
ID Code:850
Deposited By:Professor Anry Nersesyan
Deposited On:11 Jun 2019 15:41
Last Modified:11 Jun 2019 15:41

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