Group theory
An important property about groups is whether the order of the elements matters when two elements are combined using the operation. Switching the order of two combined elements typically gives a different result. This means that we have many cases with a • b ≠ b • a. However, if the order of a and b actually does not matter (for any a and b, we always have a • b = b • a), then the group is called an abelian group (or commutative group).