Hypergroup definition and five key examples

Insights into Mathematics

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We state a precise definition of a finite commutative hypergroup, and then give five important classes of examples, 1) the class hypergroup of a finite (non-commutative) group G 2) the character hypergroup of a finite (non-commutative) group G 3) the hypergroup associated to a distance-transitive graph 4) double coset hypergroups arising from Gelfand pairs and 5) automorphism orbit hypergroups.

It will take some explaining to bring all these important families into proper focus, and show how they are useful potential tools for physicists and chemists trying to apply Diffusion Symmetry ideas to their subjects.