Independence of the Axioms of Hypergroup over the Group

Abstract

The independence of the axioms of hypergroup over the group is proven. 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 $\Lambda$.