Starting to explore

Welcome to the first Group Explorer 2 tutorial! This first tutorial is designed to give you both motive and opportunity to begin your own explorations. I'll start with a tour of the major visuals GE2 offers, and then give a description of the most useful features.

This page is meant to be a springboard, so don't hesitate to follow any of the (many) links below, even if you haven't read this whole page. That's the point of this tutorial--to help you start to explore.

Pictures Group Explorer gives four ways to answer the question "What does a group look like?" This is its primary aim and the reason for its creation. The multiplication table is the simplest way to picture a group, and explicitly shows the group operation. Definition of a multiplication table Introduction to multiplication tables (Getting Started pages) Basic manipulations of a multiplication table (Tutorial) Complete information about the multiplication table interface (User Manual) Groups describe symmetry, sometimes the symmetry of three-dimensional objects. Thus these objects have the symmetry the group describes. Definition of an object of symmetry Complete information about the object of symmetry interface (User Manual) Cayley diagrams show the group as a graph of elements interacting with each other. They show the group's structure very well, exemplifying Cayley's theorem by showing how the group acts on itself. Definition of a Cayley diagram Introduction to Cayley diagrams (Getting Started pages) Basic manipulations of a Cayley diagram (Tutorial) Complete information about the Cayley diagram interface (User Manual) Cycle graphs show an important relationship among the elements of the group by exhibiting the group's orbits. Definition of a cycle graph Complete information about the cycle graph interface (User Manual)

Features Here are some of the most important things not to miss about how Group Explorer makes group theory more accessible and intuitive. Each picture of a group is very interactive. Study properties of the group by reorganizing a diagram or highlighting it in different ways. Save useful views as images to use in a report or on a web page. Group Explorer comes with a vast library of groups, the main window that loads when you open the software. This is very hand for learning by example, for testing conjectures, and getting one's hands dirty in the real subject matter of group theory. Each group in the library, when double-clicked opens a group info window, full of useful information about the group. Many portions of the software contain links to useful explanations. Not only is the help system very robust, but group info windows contain many links, some within themselves, others to the help documentation, and others which dynamically generate illustrations for you! Furthermore, each visualizer has a help button to take you directly to the help for that visualizer. You need not be content with examining groups in isolation. Sheets are a very important new concept in this version of Group Explorer, enabling you to create homomorphisms between groups, see complex diagrams like subgroup lattices, and more.

Quick help links:
Contents | Getting Started | Tutorials | User Manual | Miscellaneous Reference
GE terminology | Help on help