A semigroup is a mathematical structure consisting of a set equipped with an associative binary operation. This means that for any three elements in the set, the way in which they are grouped during the operation does not affect the outcome. For example, if you have elements a, b, and c, then (a * b) * c = a * (b * c), where * represents the binary operation. Semigroups are important in various areas of mathematics, including algebra and computer science. They can be used to model systems where combining elements is necessary, such as in the study of automata or formal languages. A specific type of semigroup, called a monoid, includes an identity element that does not change other elements when combined.