If A is a set, then a subgroup H of S A is transitive on A if for each a, b A there exists H such that (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 ...

Let A a 1 a 2 a n Let S A be defined by a i a i 1 f ...

If A is a set, then a subgroup H of S A is transitive on A if

Question:

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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