Abstract:
The polygroup concept has found applications in many branches of mathematics such as analysis, algebra, geometry and fuzzy sets. The notion of quasi-canonical hypergroup called polygroup, which is a generalization of the notion of a group. A hyper-structure admits more than one output under the operation, which is called a hyper-operation. We generalize the notion of polygroup structure induced by the double cosets, which is also a generalization of the group object. There are only a few studies that have developed polygroup under hyper-operation. In our previous work, some of its properties such as normal subpolygroups, maximal subpolygroups and chain conditions were proved. In this paper, we construct a new polygroup from a given polygroup. Also, we show that if G, KandH are polygroups, then G∕∕H∕∕K∕∕H≅G∕∕K which is induced by the double cosets of a group.
