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. Cyclic groups can be finite or infinite, depending on whether the generator can produce a limited or unlimited number of distinct elements. 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 indicates the number of elements. An example of a cyclic group is the set of integers under addition, which can be generated by the number 1.