g is cyclic if and only if?
If G is a group of order n, G is cyclic iff G has an element of order n. If Let a∈G have order n. ... Since there are n elements in this set, and G has order n, G cannot have any other elements, and ⟨a⟩ = G, which makes G cyclic. Only If If G is cyclic, then it has a generator, b.