Finite Commutative Hypergroups and Applications from Group Theory to Conformal Field Theory

Finite abelian groups are among the most simple and useful of all algebraic ob jects possessing a pleasant but non trivial classi cation a perfect theory of duality and a penchant for cropping up in interesting places When one thinks of generalizations of this theory within the nite setting the theory of non abelian nite groups immediately comes to mind This theory has now achieved a very high state of development and sophistication It comes as a surprise perhaps that there is another generalization whose simplicity and range of application rivals that of the non abelian groups This is the theory of nite commutative hypergroups