A survey of half-groups

Abstract

In this paper, we introduce the idea of half-groups. This is an absolutely new idea and deserves significant consideration. We have imposed a group structure on a half groupoid wherein we have an identity element and each element having a unique inverse under the specified operation, then, at that point, we addressed half groups, subhalf-groups, and normal subhalf-groups. All of the fundamentals discussed in this research were backed by instances and lemmas to demonstrate their validity.