Subpolygroup Structure of a Polygroup Induced by the Double Cosets of a Group

Abstract

A polygroup is a multivalued algebraic structure satisfying the group like objects. In recent years, polygroups have been investigated by a number of mathematicians because, the notion of polygroup, in some sense, generalize the idea of a group. In this paper, we introduce some properties of polygroup structure generated by the double cosets of any given group. Besides, we investigate several results and prove some results induced by the double cosets of any given group. Furthermore, the relationship between the induced polygroup structure and corresponding group in detail. Polygroup structure has some applications in various mathematics field. Further, certain results regarding normal subpolygroups, maximal subpolygroups and subpolygroup satisfying chain conditions were proved.