This article aims to create commutative hyperstructures, starting with a non-commutative group. So, we consider the starting group to be the dihedral group Dn, with n a natural number, n>1, and we determine the HX groups associated with the dihedral group. For a fixed number n, let Gn be the set of all HX groups. In this paper, we analyze this new structure's properties and find a connection between the divisors of n and the cardinality of Gn. Moreover, this new structure is commutative.
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A way to construct commutative hyperstructures
Published: 28 April 2023 by MDPI in The 1st International Online Conference on Mathematics and Applications session Algebra and Geometry with Applications to Related Fields
Keywords: HX groups, commutative, dihedral group, hyperstructure