Let X and Y be G-scts with the same group G. An isomorphism between G-sets X and Y is a map ϕ : X → Y that is one to one, onto Y, and satisfies g ϕ(x) = ϕ(gx) for all X ∈ X and g ∈ G. Two G-sets are isomorphic if such an isomorphism between them exists. Let X be the D4-set of Example 16.8.
a. Find two distinct orbits of X that are isomorphic sub-D4-sets.
b. Show that the orbits {1,2, 3, 4} and [s1, s2, s3, s4} are not isomorphic sub-D4-sets. [Hint: Find an element of G that acts in an essentially different fashion on the two orbits.]
c. Are the orbits you gave for your answer to part (a) the only two different isomorphic sub-D4-sets of X?
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.