The following is a proof that all cyclic groups are abelian.
Proof. Let $G$ be a cyclic group and $g$ be a generator of $G$ Let $a,b \in G$ Then there exist $x,y \in {\mathbb Z}$ such that $a=g^x$ and $b=g^y$ Since $ab=g^xg^y=g^{x+y}=g^{y+x}=g^yg^x=ba$ it follows that $G$ is abelian.
"proof that all cyclic groups are abelian" is owned by Wkbj79.
![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
