Hypergroups and their pullback and pushout structures

Abstract

Hypergroups in the sense of Marty are very important and a rather difficult subject to be understood since they do not generally have any identity or inverse element. Crossed modules are one of the most important tools to be applied on groups. In this study, we combine hypergroups and crossed modules to obtain the crossed modules of the hypergroups. We shortly present hypergroups with their properties and examples. In addition two important applications of crossed modules are given. These applications are about pullback and pushout crossed module of hypergroups and their properties. The denition of hypergroups generated by sets plays vital roles throughout the paper.

Keywords

• Action,Crossed module,Hypergroup,Fundamental relation,Pull- back,Pushout

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