Independence of the axioms of hypergroup over the group
DOI:
https://doi.org/10.52737/18291163-2021.13.12-1-11Keywords:
Hypergroup over the group, axioms, independenceAbstract
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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