A cyclic group is a type of mathematical group that can be generated by a single element. This means that every element in the group can be expressed as a power of this generator. For example, if g is the generator, then every element in the cyclic group can be written as g^n for some integer n. Cyclic groups can be finite or infinite, depending on whether the generator has a finite order. Cyclic groups are important in various areas of mathematics, including abstract algebra and number theory. They are often denoted as Z_n for finite groups, where n is the number of elements, or as Z for the infinite group of integers under addition. Their simple structure makes them a fundamental building block in group theory.