Exercises through show how all possible G-sets, up to isomorphism (see Exercise 9), can be formed from the group G. Let X be a transitive G-set, and let xo ∈ X. Show that X is isomorphic (see Exercise 9) to the G-set L of all left cosets of Gx0, described in Example 16.7. [Hint: For X ∈ X, suppose X = gxo, and define ϕ : X → L by ϕ(x) = gGx0. Be sure to show ϕ is well defined!]
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