A New Type of Weakly Commutative Groups

TL;DR

This paper introduces Wm-groups, a new class of algebraic structures with specific axioms, and explores their fundamental properties, including subgroups, homomorphisms, and quotient structures.

Contribution

It defines Wm-groups with semi commutativity, right identity, and left inverse, and develops their basic theory and related concepts.

Findings

Defined Wm-groups with specific axioms

Established properties of subgroups and homomorphisms

Analyzed quotient structures and normal subgroups

Abstract

The aim of the present paper is to define and study a new class of groups, namely Wm-groups with a single binary operation based on axioms of semi commutativity, right identity and left inverse. Moreover, we introduce the notions of right cosets, quotient Wm-groups, homomorphisms, kernel and normal Wm-subgroups in terms of Wm-groups, and investigate some of their properties.