Question

In: Advanced Math

Let G act transitively on Ω and assume G is finite. Define an action of G...

Let G act transitively on Ω and assume G is finite. Define an action of G on the set Ω × Ω by putting

(α,β) · g = (α · g, β · g).

Let α ∈ Ω Show that G has the same number of orbits on Ω × Ω That Gα has on Ω

Solutions

Expert Solution

For the proof, at first a lemma has been proved using the transitivity of the action of G on . Then this lemma has been used to exhibit a bijection between the two respective orbit sets, which proves the given result.


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