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Group Explorer is mathematical visualization software for the abstract algebra classroom. It helps the user visualize group theory, builds students' intuition, and enables experimentation with groups.

Features:

* Displays Cayley diagrams, multiplication tables, cycle graphs, and objects with symmetry
* Many common group-theoretic computations can be done visually
* Compare groups and subgroups via morphisms (see illustration below)
* Browsable, searchable group library
* Integrated help system (which you can preview on the web)
* Save and print images at any scale and quality

Group Explorer helps you visualize groups, homomorphisms, subgroup lattices, and more. Main features are introduced here, but the help system is far more in-depth, fully cross-referenced with definitions of key terms and hyperlinks that create illustrations for you. This page only scratches the surface.

Multiplication Tables

The most common group visualization technique is the multiplication table; nearly every student has seen it and therefore it needs little introduction.

Cayley Diagrams

Cayley diagrams are a very potent but underused visualization technique, probably because creating them is difficult by hand. Group Explorer makes them easy to view and edit.

Cycle Graphs

Cycle graphs show all the orbits in a group and the intersections among them.

Symmetry Objects

Many small, finite groups describe the symmetries inherent in physical objects. Group Explorer's group library contains 3D visualizations of these objects for every such group.

Sheets

Group Explorer can also illustrate homomorphisms and collections thereof in documents called sheets. You can edit sheets by dropping in your own group visualizations, homomorphisms, captions, and headings. Or let Group Explorer auto-generate a sheet to answer a specific question.