UNIFICATION OF MULTIGROUPS AND MULTISET GROUPS

Abstract

This paper presents a unified approach to studying multigroup and multiset group by examining their structural relationships within a common algebraic framework. The work investigates the connection between these two generalized group concepts and establishes that every multigroup is a multiset group, while the converse does not necessarily hold. This observation motivates a new paradigm at the intersection of multigroup and multiset group theory: the multigroup set. The proposed approach provides a broader multiset context for understanding group-like structures and offers a unified perspective that captures the essential properties shared by both concepts. This study contributes to the ongoing development of multiset-based algebraic structures and opens new directions for further research.