Direct Product Groups

There are two initial choices under this menu:

  • Zn Direct Products
  • Make New Direct Product.  

If you select Zn Direct Products, you then enter two numbers for Zn groups, such as Z2 and Z3, as illustrated in the top right box.

Each product table displays with a key which shows the ordered pair that each element in the table repesents, as illustrated on the right.

If you want ordered pairs to display in the table, go to Edit Menu and click on Change Detail. To go back to condensed form, click on Change Detail again.

When you select Make New Direct Product, a box displays whose drop-down menus list all open tables. You then select two tables. To create D3 x Z2, you must first open the tables for D3 and Z2.

You can create multiple direct products in this manner. For example, if Z2 and Z2 x Z3 are open, you can then create Z2 x Z3 x Z2, as illustrated on the right.

If your direct product gets too big, GU will lose some of its functionality. It may not be able to display the table, or it may be able to display the table, but not the lattice.

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