Concept of Anti Multigroups and its Properties

Abstract

The concept of multigroups is an application of multiset to group theory. Multigroup is an algebraic structure of a multiset whose underlying set is a group. The objective of this paper is to introduce the concept of anti multigroups and deduce some related results. We establish that a multiset defined over a group is a multigroup if and only if its complement is an anti multigroup. Finally, some results that connect cuts of multigroups to anti multigroups are considered.