Visualization of finite groups: The case of the Rubik's cube and supporting properties in GeoGebra

Abstract

In this text, we present a discussion about the Rubik's Cube and its relationship with Group Theory, particularly permutation groups, as well as possibilities for exploring it using the GeoGebra software interface. We bring a brief discussion about the concept of group, aspects of the Rubik's cube, the Rubik's group as a group of permutations and possibilities for its exploration in GeoGebra. Based on this study, we recognize the potential to delve into permutation groups in Abstract Algebra through a visual interface that associates their properties with a tangible and manipulable object. Additionally, there is the potential for simulating their movements using Dynamic Geometry software, such as GeoGebra. These findings highlight the relevance of GeoGebra as a useful tool for visualizing and understanding permutation groups, promoting a more intuitive and accessible approach to Group Theory in the educational context.

Keywords

• rubik's cube
• group theory
• permutation groups
• geogebra