Referring to Exercise 49 of Section 8, show that H of Exercise 37 is transitive on the set G Data from Exercise 37 Show that H a a G is a subgroup of S G , the group of all permutations of G Data from Exercise 49 of Section 8 If A is a set, then a subgroup H of S A is transitive on A if for each a,...

Referring to Exercise 49 of Section 8, show that H of Exercise 37 is transitive on the

Question:

Referring to Exercise 49 of Section 8, show that H of Exercise 37 is transitive on the set G.

Data from Exercise 37

Show that H ={ γ_a | a ∈ G} is a subgroup of S_G, the group of all permutations of G.

Data from Exercise 49 of Section 8

If A is a set, then a subgroup H of S_A is transitive on A if for each a, b ∈ A there exists σ ∈ H such that σ(a) = b. Show that if A is a nonempty finite set, then there exists a finite cyclic subgroup H of S_A with |H|= |A| that is transitive on A.

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