2065

Enumeration of KH-Hyperstructures related with Hv-(semi)groups and Semihypergroups and Hyperstructures dependent on it

دكتري تخصصي

رياضي محض گرايش ابرجبرها و جبرهاي مرتب شده

مركز تحصيلات تكميلي دانشگاه پيام نور

1402

1402/06/27

دكتر سعيد ميروكيلي، دكتر بيژن دواز

Polysymmetrical hypergroup, Complete hypergroup KH-Hv-group, (H, Poly(P))- Hypergroup, Enumerate, Polygroup

In algebraic hyperstructures, there are methods to construct a larger hyperstructure from a smaller hyperstructure, which cannot be implemented in classical algebraic structures. For example, complete hypergroup, KH-hypergroup, (H,G)-hypergroup, constructing polysymmetric hypergroup and extension of polygroups by polygroups with methods that are not possible in group theory. In this thesis, the hyperstructures of KH-Hv-group and (H, Poly(P))- hypergroup are studied. A KH-Hv-group is constructed from a Hv-group, and this type of construction is a generalization of the KH-hypergroup. Enumerating algebraic hyperstructures by analytical methods is one of the interesting topics in this theory. In this thesis, KH-Hv-(semi)groups of order n, which are counted from Hv-(semi)groups of order two, are completely enumerated. Next, the hyperstructure of (H, Poly(P))-hypergroup is studied and compared with the hyperstructures of KH-hypergroup, (H,G)-hypergroup and the extension of polygroups by polygroups. Also, polysymmetric semihypergroups and complete semihypergroups made of semigroups of small order are computed.

1403/03/18

ابراهيمي

75871