A Visual Approach to Group Homomorphisms Using GeoGebra

Renata Teófilo de Sousa; Francisco Régis Vieira Alves; Ana Paula Florêncio Aires

Archives · Vol. 13, No. 1 (2025)

A Visual Approach to Group Homomorphisms Using GeoGebra

Renata Teófilo de Sousa, Francisco Régis Vieira Alves, Ana Paula Florêncio Aires

Renata Teófilo de Sousa — Ceará State Department of Education

Francisco Régis Vieira Alves — Federal Institute of Education, Science, and Technology of Ceará

Ana Paula Florêncio Aires — University of Trás-os-Montes and Alto Douro – UTAD

↓ Download PDF pp. 18–26

Abstract

This article, excerpted from an ongoing doctoral research project, presents a visual approach to the study of group homomorphisms using GeoGebra as a tool for construction and exploration. Focusing on the classical homomorphism from the symmetric group S3 to the cyclic group Z2, the study analyzes two distinct visual representations---one in 2D and the other in 3D. These constructions highlight fundamental algebraic properties such as kernel, image, and cosets, while also illustrating the preservation of operations and offering an intuitive application of the First Isomorphism Theorem.

Keywords: Group Homomorphisms, GeoGebra, Mathematics Visualization

Licensed under CC BY-NC-SA 4.0 · ISSN 2162-3856 · North American GeoGebra Journal