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, the group consists of elements like g^0, g^1, g^2, and so on. Cyclic groups can be finite or infinite, depending on whether the generator has a finite order. Cyclic groups are fundamental in group theory, a branch of abstract algebra. They are denoted as \mathbbZ_n for finite groups, where n is the number of elements, or \mathbbZ for infinite groups. Examples of cyclic groups include the integers under addition and the set of roots of unity in complex numbers, which are related to complex analysis.