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Permutation Groups

A permutation of a set is a 1-1 function that maps the set onto itself. Under Permutation Groups, select Sn or An.

  • Sn is the set of all permutations of 1, 2, 3, . . . , n under function composition.

  • An is the set of all elements in Sn that can be represented as a product of an even number
    of 2-cycles.

If you select Sn, the box on the right displays with S selected. You can only enter 3 or 4.  S5 has too many elements to implement in GU. You can display the tables for A3, A4, and A5, which has 60 elements. GU will find all subgroups of A5 and also display its lattice.

When you open a permutation group, the table and a key display, which shows the permutation represented by each letter in the table. If you want cycle notation to display in the table, go to the Edit Menu and click on Change Detail. To go back to condensed form, click on Change Detail again.

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