  On the transversals of a subgroup of a group, using the binary operation of
the group, structural mappings are defined. Based on these mappings, the notion
of the hypergroup over the group is introduced, which generalizes the notion of
the quotient-group of the given group with respect to the normal subgroup. The
category of the hypergroups over the group contains as subcategories the
category of groups, the category of linear spaces, the category of fields.
