Armenian Journal of Mathematics, 13(12)
2021; 1–11
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Independence of the axioms of hypergroup over the group

Shant Navasardyan*

Received: 2024-12-10 · Published: 2021-12-21

© 2021 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
Independence of the axioms of hypergroup over the group
Author
Shant Navasardyan
Source journal
Armenian Journal of Mathematics, 13(12)
Published
2021-12-21
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2021.13.12-1-11

Abstract

The independence of the axioms of hypergroup over the group is proved. The proof is composed of two parts. In the first part, the independence of the axioms (P3)(P3), (A1)(A1), (A3)(A3), (A5)(A5) in the system of axioms of hypergroup over the group is shown by fixing the structural mappings ΦΦ and ΞΞ. In the same way, in the second part of the proof, the independence of the axioms (P1)(P1), (P2)(P2), (A2)(A2), (A4)(A4) is shown by fixing ΨΨ and ΛΛ.
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