A Study on the Importance of Cyclic Group: Exploring the Properties of Cyclic Groups

Abstract

A cyclic group is a group that isgenerated by a single element, in the sense that every element of the group canbe 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 thegroup operation. Any finite cyclic group of order n is isomorphic to Z/nZ, the integers modulo n with addition as the group operation.