Repeat the preceding exercise, but find the right cosets this time. Are they the same as the left cosets?

Data from Exercise 6 

Find all left cosets of the subgroup {p₀ , µ₂} of the group D₄ given by Table 8.12.

Table 8.12

 

Transcribed Image Text:

Po PI P2 P3 f 14₂ 8₁ 82 Po PI P₂ P3 μ| 12 8₁ Po Pi P2 P3 μ P₁ P2 P3 P3 M2 P2 P3 Po P₁ f42 MI 20 8₂ Po 8₁ fly 82 8₁ μl) 12 P₁ P2 Pi 8₁ f₂ 3 8₂ Po 8₁ 8₁ ळ £ 12 12 8₁ 8₂ fly 3 82 P2 Po 82 8₁ P3 1₂ 8₂ 82 8₂ PI μ₁ E Po P2 P3 P1 8₁ flj 12 P3 Pi P3 Po P2 PI P2 Po