On Unitary Hypergroups over the Group

Abstract

A concept of the unitary hypergroup MH over the group is introduced. If for a given set M and a group H all unitary hypergroups MH over the group, up to isomorphism, are known, a method is proposed to construct all hypergroups MH over the group, up to isomorphism. It reduces the problem of description of all hypergroups over the group, up to isomorphism, to the problem of description of all unitary hypergroups over the group, up to isomorphism, and can have many other applications. When M and H are finite, a formula is obtained, which connects the numbers of elements in the classes of isomorphism of all hypergroups over the group and of all unitary hypergroups over the group.