Groups15 and Groups32

This system provides information about groups of order 1-32.  This is the original application, written in Forth, which was used as the basis for the Groups15 demo. Groups32 is accessible via Telnet. (The telnet version is not programmable, however).

Click here for the Groups32 website. The website also contains a variety of written material.

Groups15 (demo)
This is a Java applet written as an experiment in making mathematical software available on the WEB. It provides information about groups of order 1-15. It does not contain all of the functions of Groups32.

Click here for instructions to run the Groups15 applet.
 For information about Groups32 and comments send email to

Groups15 Demo

          Set your browser to full screen or use a large window.

      1. Use the slider to select a group (order 1-15)
      2. Press the EleOrd button to see the elements listed by order
      3. Press the Subgroups button to see a list of subgroups
      4. Press the Cosets button to see the left and right cosets of the highlighted subgroup
      5. The Eval button lets you evaluate strings in the group letters and their inverses for the currently selected group. Notice that Eval is case sensitive and only accepts letters belonging to the current group.  Press ENTER to evaluate the string.

        Click here to start the  Demo