Theory of disguised-groups

TL;DR

This paper introduces disguised-groups, a new algebraic structure that aligns with regular semigroups, and adapts group theory results to this context, revealing new insights in algebra.

Contribution

It defines disguised-groups, proves their equivalence to regular semigroups, and extends group theory results to this novel structure.

Findings

Disguised-groups coincide with regular semigroups

Many group theory results are adapted to disguised-groups

New results in the theory of regular semigroups are established

Abstract

In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the results of the theory of groups adapted to this case and some unknown results in the theory of groups and regular semigroups.