In mathematics, the term "abelian" refers to a specific type of group in group theory, named after the mathematician Niels Henrik Abel. An abelian group is one in which the order of the elements does not affect the outcome of the operation. This means that for any two elements a and b in the group, the equation a * b = b * a holds true, indicating that the group operation is commutative. Abelian groups are fundamental in various areas of mathematics, including algebra and number theory. Examples of abelian groups include the set of integers under addition and the set of real numbers under addition. These groups are essential for understanding more complex structures and play a crucial role in many mathematical theories.