Compute the left regular representation of Z₄ . Compute the right regular representation of S₃ using the notation of Example 8.7.

Data from Example 8.7.

An interesting example for us is the group S3 of 3! = 6 elements. Let the set A be { 1, 2, 3}. We list the permutations of A and assign to each a subscripted Greek letter for a name.

The reasons for the choice of names will be clear later. Let 

Transcribed Image Text:

Po = P1 = P₂ = 1 2 12 3 2 3 1 2 3 2 3 1) 1 2 3 3 1 2 M₁ = 1₂ = Из = 1 1 2 3 3 2 (123) 2 (173) 2