Consider the group S₃ of Example 8.7 

a. Find the cyclic subgroups (p₁), (p₂), and (µ₁) of S₃. 

b. Find all subgroups, proper and improper, of S₃ and give the subgroup diagram for them.

Data from Example 8.7

An interesting example fo rus 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:

2 PO = (1 ₂²3). Po 2 P1 = 1 2 3 2 3 1 2 3 - (²) 3 1 2 P2 = (1 = - (1 32). H2 = из 1 2 3 2 1 2 3 1, 2 3 1 3