Python Implementation and Construction of Finite Abelian Groups

TL;DR

This paper introduces a Python framework for constructing and exploring finite abelian groups, combining computational tools with theoretical results to aid students in understanding algebraic structures.

Contribution

It provides an open-source implementation for finite abelian groups in Python, integrating number theory and computational methods for educational purposes.

Findings

Implementation of finite abelian groups using modular operations

Inclusion of direct products of cyclic groups

Demonstration of blending number theory with computation

Abstract

Here we present a working framework to establish finite abelian groups in python. The primary aim is to allow new A-level students to work with examples of finite abelian groups using open source software. We include the code used in the implementation of the framework. We also prove some useful results regarding finite abelian groups which are used to establish the functions and help show how number theoretic results can blend with computational power when studying algebra. The groups established are based modular multiplication and addition. We include direct products of cyclic groups meaning the user has access to all finite abelian groups.