Abelian Groups
Definition: Abelian Group
A group \((G, \cdot)\) is called abelian, if its operation is commutative:
\[ a \cdot b = b \cdot a \qquad \forall a,b \in G \]
Theorem: Criterion for Abelian Groups
Let \((G, \cdot)\) be a group.
If \(g^2 = 1\) for all \(g \in G\), then \((G, \cdot)\) is abelian.
Proof
TODO