A Visual Approach to Group Homomorphisms Using GeoGebra

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Published: Jul 13, 2025
Keywords:
Group Homomorphisms, GeoGebra, Mathematics Visualization

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Renata Teófilo de Sousa
Ceará State Department of Education
https://orcid.org/0000-0001-5507-2691
Francisco Régis Vieira Alves
Federal Institute of Education, Science, and Technology of Ceará
https://orcid.org/0000-0003-3710-1561
Ana Paula Florêncio Aires
University of Trás-os-Montes and Alto Douro – UTAD
https://orcid.org/0000-0001-8138-3776

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.

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Vol. 13 No. 1 (2025): North American GeoGebra Journal
Section
Articles
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Author Biographies

Renata Teófilo de Sousa, Ceará State Department of Education

PhD student in Teaching, specializing in Mathematics Teaching (RENOEN/IFCE). Master’s in Science and Mathematics Teaching from the Federal Institute of Education, Science, and Technology of Ceará – IFCE Fortaleza campus. Specialist in Mathematics Teaching (UVA), Qualification in Mathematics Teaching in the State of Ceará (UFC), Didactics and Active Learning Methodologies, MBA in School Management (UniAmérica). Specialist in Neuropsychopedagogy. Teacher at the Ceará State Department of Education.

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

PhD in Education from the Federal University of Ceará, CNPq productivity scholarship holder – PQ2 (2020–2026). Permanent professor of the Graduate Program in Science and Mathematics Teaching (PPGECM/IFCE). Permanent professor of the Graduate Program in Science and Mathematics Teaching at the Federal University of Ceará (ENCIMA/UFC). Permanent professor of the Graduate Program in the Professional Master's in Technological Education (PROFEPT). Full professor at the Federal Institute of Education, Science, and Technology of Ceará – Department of Mathematics and Physics. Professor in the Doctorate in Teaching of the Northeast Teaching Network (RENOEN, IFCE campus). Leader of the CNPq Research Group on Science and Mathematics Teaching and Engineering Teaching.

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

PhD in Mathematics Education, with a specialization in Didactics of Mathematics from the University of Salamanca. Member of the Research Center on Didactics and Technology in Teacher Training (CIDTFF) – University of Aveiro. Associate Professor in the Department of Mathematics at the University of Trás-os-Montes and Alto Douro (UTAD). Research interests include the following areas: Didactics of Mathematics; History of Mathematics Education; History of Mathematics; Professional Teaching Practices; ICT in Mathematics Teaching and Teacher Training; Number Theory.