Isoclinism of crossed modules

TL;DR

This paper introduces the concept of isoclinism for crossed modules, providing theoretical foundations and practical GAP implementations to classify and enumerate isoclinic finite crossed modules.

Contribution

It defines isoclinism for crossed modules and offers computational tools for classification and enumeration within the GAP system.

Findings

GAP implementations for constructing isoclinism families

Enumeration of isoclinic crossed modules in the GAP library

Framework for classifying crossed modules based on isoclinism

Abstract

We introduce the isoclinism of crossed modules. We also give GAP implementations for constructing the isoclinism families of finite crossed modules and consequently give an enumeration about isoclinic crossed modules existing in the GAP library.