Duality in the theory of finite commutative multivalued groups

The purpose of this paper is to construct a duality theory for finite commutative multivalued groups and to demonstrate its connection with the classical duality in the theory of ordinary groups and the Kawada–Delsarte duality in algebraic combinatorics. We study in detail the case of multivalued groups of order three, construct a parameterization of the set of these groups, and obtain explicit formulas for the duality. In future, we plan to use this duality in the study of the coset problem. Bibl. 26 titles.