On Isotopic Characterization of Central Loops

TL;DR

This paper investigates the isotopic properties of central loops, constructs finite C-loops, and demonstrates that certain isotopisms preserve central identities, contributing to the algebraic understanding of loop structures.

Contribution

It introduces new results on isotopic invariance of central identities and provides a method to construct finite C-loops based on representation sets.

Findings

Central identities are isotopic invariant under specific isotopisms

Construction of finite C-loops from representation sets

Enhanced understanding of isotopic properties of central loops

Abstract

The representation sets of central loops are investigated and the results obtained are used to construct a finite C-loop. It is shown that for certain types of isotopisms, the central identities are isotopic invariant.