Up to isomorphism, how many transitive Z₄ sets X are there? Give an example of each isomorphism type, listing an action table of each as in Table 16.10. Take lowercase names a, b, c, and so on for the elements in the set X.

Data from Table 16.10

Transcribed Image Text:

Po P1 1 με 8₁ 8₂ 1234 P2 P3 fl 2 1 AN 2 3 234 31 1 4 3 3 2 1 4 3 4 4 4 1 1 2 2 3 4 3 2 1 3 142 4 2 $1 $2 S1 $2 $2 S3 $3 S4 S4 S1 $3 $2 S4 $3 $4 $1 S4 S3 S4 S4 S₁ $2 $3 S2 S4 S3 $1 S1 S2 S3 $2 $1 $1 S4 S3 $2 d₂ C P₁ P₂ d₂ C P₁ P₂ d₁ C P₂ d₂ C MI d₁ C m1 m2 d₁ C P₁ MI M2 d₂ C P₁ d₁ m₂ MI d₁ с d₂ m2 m1 d₁ d₂ C M₁ m1 M₂ m1 M₂ M2 m2 m1 M₂ d₁ d₁ d₂ d₁ d₂ d₂ P3 P₂ P4 P3 P₁ P₁ P4 P3 P3 P3 P4 P₁ P₂ P₁ P3 P₂ P₁ P₁ P4 PA P₁ P₂ P3 P₂ PA P4 P3 P₂ P₁