Let a be an element of a group G. The elements a^r, where r is an integer, form a subgroup of G, called the subgroup generated by a and denoted ⟨a⟩. A group G is cyclic if there is an element a in G such that ⟨a⟩ = G. If G is a finite cyclic group with identity e, then G = {e, a, a²,…, aⁿ⁻¹}, where n is the order of a. If G is an infinite cyclic group, then G = {…, a⁻², a⁻¹, e, a, a²,…}. Any two cyclic groups of the same order are isomorphic. Every subgroup of a cyclic group is cyclic.