On Some Properties of Multigroups

In this paper, we studied some algebraic properties of multigroups. Some of the properties of multisets have also been studied. We discovered that for any multiset G to be a multigroup over the group X, then its count function C_G must satisfies the two conditions: (i) C_G (xy)?[C_G (x)? C_G (y)],? x,y?X; (where ? is the minimum operation). (ii) C_G (x^(-1) )?C_G (x), ? x?X. We also discovered that if X is a group and A,B?MG(X), then A?B?MG(X) but A?B?MG(X). It has also been shown that if A and B are two multigroups over a group X, then A is said to be a submultigroup of B if A?B. Hence, the study shows that the theory of multisets and multigroups can be very useful in many areas such as information retrieval on the web, data mining, decision making, data encryption, coding theory etc.