Vol. 13 No. 12 (2021): Independence of the axioms of hypergroup over the group

Published: 2021-12-21

Articles

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    Independence of the axioms of hypergroup over the group

    Shant Navasardyan
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    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 $(P3)$, $(A1)$, $(A3)$, $(A5)$ in the system of axioms of hypergroup over the group is shown by fixing the structural mappings $\Phi$ and $\Xi$. In the same way, in the second part of the proof, the independence of the axioms $(P1)$, $(P2)$, $(A2)$, $(A4)$ is shown by fixing $\Psi$ and $\Lambda$.

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