Rewrite Table 8.12 in the order exhibited by the left cosets in Exercise 9. Do you seem to get a coset group of order 4? If so, is it isomorphic to Z₄ or to the Klein 4-group V?

Data from exercise 9 

Repeat Exercise 6 for the subgroup {P_o, p₂} of D₄.

Table 8.12

Transcribed Image Text:

Po PI P2 P3 12 8₁ Po 8₂ Po μ₁ fly P1 Pi P2 P3 M₂ 8₁ 12 P2 P3 Po 8₁ 82 μ2 fl Po PI μ2 82 8₁ P3 Po PI P2 82 P2 P3 P₁ P2 82 12 8₁ 8₁ fly μls P3 8₂ μ₂ 8₂ 3 12 8₁ P2 fl 8₂ 12 8₁ Po P2 P3 PI ळ 8₁ Po 82 12 PI P3 8₂ MI M2 Po PI P3 P2 12 8₁ μ1 P3 P1 P2 Po