Semidirect Product of Loops with Groups

TL;DR

This paper investigates loops formed as semidirect products of loops and groups, analyzing their algebraic structures including commutants, nuclei, and centers.

Contribution

It introduces the concept of semidirect product loops and explores their structural properties, which is a novel approach in loop theory.

Findings

Characterization of the commutant of semidirect product loops

Analysis of nuclei and centers in these loops

Structural properties derived from the semidirect product construction

Abstract

In this paper, we have studied the loops which are the semidirect products of a loop and a group. Also, the cummutant, nuclei and the center of such loops are studied.