Referring to the group S₃ given in Example 8.7, compute the product (0_P0 + 1_p1 + 0_P2 + 0_µ1 + 1_µ2 + 1_µ3)(1_p0 + 1_P1 + 0_P2 + 1_µ1 + 0_µ2 + 1_µ3) in the group algebra Z₂S₃.

Data from in 8.7 Example 

An interesting example for us is the group S₃ of3! = 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:

ро = P1 P2 - (123) (133) ( 1 3 2 3 1 2 " " M1 = М2 = из = 1 1 2 3 3 2 (123) (273)