Armenian Journal of Mathematics, 11(9)
2022; 1–27
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Quasigroups, Units and Belousov's Problem # 18

Aleksandar Krapež*, Victor Shcherbacov

Received: 2024-12-11 · Published: 2022-09-15

© 2022 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Quasigroups, Units and Belousov's Problem # 18
Authors
Aleksandar Krapež, Victor Shcherbacov
Source journal
Armenian Journal of Mathematics, 11(9)
Published
2022-09-15
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2019.11.9-1-27

Abstract

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.
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