Friday, June 14, 2024

Solution to Simple Permutation Group Problem

 Let A = {1, 2, 3, 4, 5} and s  be the result (st)  

 Find: 1 t, 2t , 3t , 4t, and 5t

Compare to:  st, 2st , 3st , 4st, and 5st

Soln.:

Let:   t =

 [1 2 3 4 5]

 [3 5 4 2 1]


1(t = 2,  2(t = 5, 3(t = 4, 4(t = 2,  5(t = 1

From def. illustration:  s = st  =  

[1 2 3 4 5]

[4 2 5 3 1] 

Then:

1(st = 4,  2(st = 2 , 3(st = 5, 4(st = 3,  5(st = 1

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