$H_v$-Normal subgroups and $H_v$-quotient groups

Abstract

‎A larger class of algebraic hyperstructures satisfying the group-like axioms is the class of $H_v$-groups‎. ‎In this paper‎, ‎without any condition and in general‎, ‎we define the $H_v$-normal subgroup and the $H_v$-quotient group of a $H_v$-group‎. ‎We introduce the fundamental equivalence relation of a $H_v$-quotient group and prove the first and third isomorphism theorems for $H_v$-groups‎.