G-Hypergroups: Hypergroups with a Group-Isomorphic Heart

Hypergroups can be subdivided into two large classes: those whose heart coincide with the entire hypergroup and in which is a proper sub-hypergroup. The latter class includes family of 1-hypergroups, reduces to singleton, therefore trivial group. However, very little known about hypergroups that are neither 1-hypergroups nor belong first class. goal this work take step classifying G-hypergroups, is, nontrivial We introduce their main properties, an emphasis on G-hypergroups torsion analyze properties stabilizers group actions heart, play important role construction multiplicative tables G-hypergroups. Based these results, we characterize type U right or cogroups right. Finally, present hyperproduct all size not larger than 5, apart isomorphisms.