Linear representation of Abel-Grassmann groups

TL;DR

This paper introduces a linear representation for Abel-Grassmann groups, enabling the enumeration of these groups up to isomorphism for orders less than 512, and improves upon previous results.

Contribution

It provides a novel linear representation for Abel-Grassmann groups, facilitating enumeration and advancing understanding of their structure.

Findings

Enumeration of Abel-Grassmann groups up to order 512

Improved previous results on Abel-Grassmann groups

Established a linear representation for these groups

Abstract

We describe an linear representation for Abel-Grassmann groups. As a consequence, we obtain or improve many previous results. In particular, enumeration of Abel-Grassmann groups up to isomorphism is obtained for orders <512.