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 (or multiple) of this generator. For example, if g is the generator, the group consists of elements like g, g^2, g^3, and so on, including the identity element. Cyclic groups can be finite or infinite. A finite cyclic group has a limited number of elements, while an infinite cyclic group continues indefinitely. These groups are fundamental in abstract algebra and have applications in various fields, including cryptography and number theory.