Give a one-sentence synopsis of the proof of Theorem 6.1.

Theorem 6.1.

Every cyclic group is abelian.

Proof Let G be a cyclic group and let a be a generator of G so that  G = (a) = {an| n ∈ Z}. 

If g₁ and g₂ are any two elements of G, there exist integers r ands such that g₁ = a^r and g₂ = a^s • Then g₁g₂ = a^ra^s = a^r+s = a^s+r = a^sa^r = g₂g₁ so G is abelian.