On Some Properties of Multigroups

• Author(s): Ewaoche Nicholas ; Samuel Henry Owoicho ; Okpanachi Sunday ; Uko Benjamin Joseph ; Okpanachi George Echiye
• Paper ID: 1710873
• Page: 1485-1490
• Published Date: 26-09-2025
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 9 Issue 3 September-2025

Abstract

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.

Keywords

Multisets, Group, Multigroups, Count function.

Citations

IRE Journals:
Ewaoche Nicholas , Samuel Henry Owoicho , Okpanachi Sunday , Uko Benjamin Joseph , Okpanachi George Echiye "On Some Properties of Multigroups" Iconic Research And Engineering Journals Volume 9 Issue 3 2025 Page 1485-1490

IEEE:
Ewaoche Nicholas , Samuel Henry Owoicho , Okpanachi Sunday , Uko Benjamin Joseph , Okpanachi George Echiye "On Some Properties of Multigroups" Iconic Research And Engineering Journals, 9(3)