prove that a group of order 3 must be cyclic

Question

formal proof needed

Answer 1

Let a, b, 1 be elements of G. By Lagrange's theorem G/⟨a⟩ has an order that divides |G|. Since ⟨a⟩ is non-trivial |G/⟨a⟩|=1 and therefore ⟨a⟩≅G.