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Morphisms

When you select Morphisms, a 2-column box displays to define a function, as illustrated on the right.

First, select the table you want for the domain and the table you want to map to. Then enter values from the second table.

To see if your entries preserve the operation, go to the upper left corner of the top menu and select:

    Check if it's a Homomorphism

 

 

 

To return to the regular menu and leave the defined function on the screen, click on a table.


When Assisted Mapping is turned on, after each entry you make, GU fills in the required values for each power of that element.  If you enter an element that cannot preserve the operation, GU will tell you so.


To make smart choices for your entries, display the lattices of the two groups or the cyclic subgroups so that you can use the orders of the elements to eliminate some of the possible entries.

 

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