Group Explorer Data File Generator

Contributed by Yuichiro Urata and Masanari Kida
University of Electro-Communications, Tokyo, Japan

In Group Explorer, you can see definitions of groups, which list a set of generators, and relations among them. Such definitions can be viewed as quotients of a free group on the generators. However, Group Explorer does not let you go in the other direction: take such definitions and produce a group.

So Yuichiro Urata has written a Java program to fill that need. He has given me permission to distribute it on this website, under the GNU General Public License. The directions below describe its use.

Download multitable.jar

Download the .jar file from the link above. Ensure you have a working Java installation on your system (and in your path). Run the program using a command like the following, issued in the same folder as the .jar file. This example will create the file D_5.group; use an appropriate name for the group for which you wish to generate a file.

% java -jar multitable.jar D_5

Then a prompt like the following asks you to input generators.

generators = 

You provide a list of elements, such as x,y. It then prompts you for the relations among them.

relations = 

You provide a list of relations, such as x*x*x*x*x,y*y,x*y*x*y. These are to be interpreted as x⁵ = e, y² = e, and xyxy = e. (In finite groups, all relations can be written in this form without use of the symbol =, nor of inverses.)

It then produces a file named D_5.group in the directory from which you ran the original java command.

You can also input a list of permutations as generators instead, and then it will not ask you for relations among them, but simply compute the group.

% java -jar multitable.jar A_7
generators = (1,2,3),(1,3,4),(1,4,5),(1,5,6),(1,6,7)