In algebra, a **cyclic group** is a group that is generated by a single element, in the sense that every element of the group can be written as a power of some particular element *g* in multiplicative notation, or as a multiple of *g* in additive notation. This element *g* is called a "generator" of the group. Any infinite cyclic group is isomorphic to **Z**, the integers with addition as the group operation. Any finite cyclic group of order *n* is isomorphic to **Z**/*n***Z**, the integers modulo n with addition as the group operation.

Read more about Cyclic Group: Definition, Properties, Examples, Representation, Subgroups and Notation, Endomorphisms, Virtually Cyclic Groups

### Famous quotes containing the word group:

“Now, honestly: if a large *group* of ... demonstrators blocked the entrances to St. Patrick’s Cathedral every Sunday for years, making it impossible for worshipers to get inside the church without someone escorting them through screaming crowds, wouldn’t some judge rule that those protesters could keep protesting, but behind police lines and out of the doorways?”

—Anna Quindlen (b. 1953)