Help window (also Group Info window)

Group Explorer help windows also play the role of Group Info windows, and therefore this page is split into two halves: Information on help windows in general and additional information for Group Info windows in particular. Both help and Group Info windows are essentially web pages, whose links not only navigate from one document to another, but can also take actions within the software. For example, a link on a help page might create for you a lattice of subgroups as an example, or a link from a Group Info window might open for you a Cayley diagram.

Help windows

Help windows essentially function like web browsers, with Back, Forward, Print, and Find buttons functioning as in all browsers. There is also a button for searching all help documents.

Copy and Save as HTML commands exist, with two caveats. First, copied text will be text only (all HTML tags removed). Second, saved HTML will have all links turned into simply underlines, and img tags will likely be broken, not only because the file is no longer in its original location, but also because some images are dynamically generated while the help page is loading within Group Explorer.

An important difference between a web browser in general and Group Explorer's help windows is that the help windows have Undo and Redo buttons. Usually web browsers are "read-only," and therefore one does not need to worry about undoing anything. However in Group Explorer, links in a help document may actually perform a change in your settings. For example, in the Group Info page for each group, there are links for adding or removing naming schemes, editing notes, etc. One can undo the changes one makes with these links using the Undo button on the help window in which one clicked the link.

The "What's this?" button appears on the help window also, but it has its own help page.

Group Info windows

Group Info windows are the presentation to the user of all information Group Explorer has about a given group. It may help you to open an example group info window now, and read it alongside this help page.

Let us consider each section that appears in a Group Info window separately. (The header and footer of each Group Info page list these sections, as links to help you navigate quickly within that page.)


The basic facts about a group are its definition, order, and any other names it has besides its primary name (which is the title of each Group Info page).


Group Explorer is all about visualization. Thus the Views section receives high priority, showing previews of every way to visualize a group, including Cayley diagrams, a multiplication table, a cycle graph, and any objects of symmetry (if the group has any).


Sometimes group file authors provide a description about the group. If the author of the group in question has done so, that information will appear here.

Computed properties

Group Explorer computes information about each group it loads. For example, it computes all of its subgroups, which ones are normal, information about conjugacy classes, and more. A summary of this information appears in the Computed properties section of the Group Info window, but much more information is available than it may seem from the summaries. Users are encouraged to click the "tell me more" links which appear in this section to find out reasons for the computations, and often many additional helpful illustrations and computations.

Related sheets

Any sheet which appears in the search paths for sheets (defined in the options window) are searched when Group Explorer opens, so that it can determine which groups are mentioned in them. On a group info page, any sheet mentioning that group will be linked to from here. This makes it easy for users to remember the existence of relevant sheets when they are examining a group, and enables you to load them with one click.

File data

This information is not mathematical information about the group itself, but rather simply information about where on your hard drive is the file from which the group was loaded.

Other definitions

If the group can be defined multiple ways, then only the primary definition was listed in the Facts section (above), and all other definitions appear here.


Group authors can provide several different lists of elements which generate the group. If they provide none, Group Explorer computes one such (minimum-size) set when the group is loaded. Each list of generators is given in this section.

Naming schemes

The structure of a group is independent of whatever symbols we use to represent the elements of the group. For this reason, a group may come with several different lists of names for its elements, and the user may choose any of them to be used as the primary way of representing the elements of the group. Hyperlinks are provided in this section for making such a selection, and for creating new user-defined naming schemes as well. User-defined naming schemes can also be removed or edited (again via the hyperlinks in this section) and this information is stored in the user's settings file. For information on the interface used for creating or editing naming schemes, refer to the documentation for that window. Changes made via hyperlinks in this section can be undone/redone using the Undo and Redo buttons at the top of the help window.


Users can add their own personal notes to a group to supplement the default information in any way they see fit. Such information appears in this section, with hyperlinks for editing it. It is text only (not HTML) and will be stored in the user's settings file. Changes made via hyperlinks in this section can be undone/redone using the Undo and Redo buttons at the top of the help window.

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