Group Explorer terminology

This page is a dictionary of terms specific to Group Explorer. Many other pages in the Group Explorer help link here to define terms. Unlike the group theory terminology page, these terms are not well-known mathematical terms; they're used only in Group Explorer.

Author of a group

The files which store group information are called group files, and they can contain information about the original author of the file. This person encoded the description of a finite group into Group Explorer's group definition syntax (using XML) so that Group Explorer could load and manipulate the group. See also Filename of a group.

Configuration file

Group Explorer stores all of your settings in a configuration file.

If you are a Windows user, then the file is called GroupExplorer.CFG, and appears in the same folder as the Group Explorer .EXE itself.
If you are a Macintosh user, then the file is ~/Library/Preferences/groupexplorer.config.
If you are a *nix user, then the file is ~/.groupexplorer.

Your configuration file contains

all the information you specify in the options window,
all notes and representations you add to a group in its info window,
and all preferences Group Explorer infers from your actions, like window positions and sizes, and the arrangement of rows and columns in the main window.

You can ask Group Explorer to use a different configuration file by passing it the command-line parameter -config.

Date of last modification for a group

The date of last modification of a group actually refers to the date on which the file from which the group was loaded was last modified. See also Filename of a group.

Filename of a group

Groups are stored in files that end in the extension .group. The group's filename is the name of the file from which the group was loaded at Group Explorer's startup. For instance, Z_2 x Z_4.group.

The default location of these files depends upon your operating system, but you can put group files anywhere you like, and then instruct Group Explorer where to look. Use the options window to tell Group Explorer where to look for group files. The group's filename does not include the path which describes the location of the group file on your machine; see Path of a group.

Naming scheme (for group elements)

See representation of a group.

Path of a group

Groups are stored in files that end in the extension .group (see Filename of a group). The group's path describes the location of the file from which the group was loaded at Group Explorer's startup. For instance, /Users/nathancarter/Development/GroupExplorer/Resources/groups/ describes a location on my hard drive where group files are located. This is an example path.

The default location of group files depends upon your operating system, but you can put group files anywhere you like, and then instruct Group Explorer where to look. Use the options window to tell Group Explorer where to look for group files.

Representation of a group

In order to display the elements of a group on the screen, Group Explorer needs to know their names. Although internally, Group Explorer stores groups in a manner consistent with the mathematical abstractions that they are, users prefer a prettier format. Each group file defines at least one representation, or naming scheme--that is, a list of names, one for each element of the group. Users can add additional representations (also called naming schemes) by using the links provided in the group info windows.

Note that group elements' representations should not be confused with group presentations, which are embeddings of arbitrary groups into groups of matrices. Group Explorer does not currently have any features related to group presentations.

Sheets

A new feature in Group Explorer 2.0, sheets are a blank canvas on which the user can drop illustrations of a group, homomorphisms to connect them, and pieces of text for description. This is a significant improvement over Group Explorer 1.5.8, in which each group could only be examined in isolation--never in comparison with other groups. There were no homomorphisms in previous versions.

To open a new sheet, from the main window, click New. You may also be interested in an introduction to sheets, or the full reference documentation on the sheet interface.

Visualizers

Group Explorer uses the term visualizer to describe any of the various mechanisms for obtaining pictures of a group. For instance, one way to visualize a group is through its multiplication table, so we refer to multiplication tables as "visualizers." Group Explorer contains four types of visualizers: multiplication tables, cycle graphs, cayley diagrams, and objects of symmetry.